CanaDAM 2013 Memorial University of Newfoundland, June 10 - 13, 2013 www.cms.math.ca//2013
 Applications of Generating Functions (CM5) Organizer and Chair: Alois Panholzer (Technische UniversitÃ¤t Wien) Starting with Leonard Euler's computation of the number of triangulations of a convex $n$-gon generating functions are an indispensable tool in combinatorial enumeration. Generating functions allow to apply algebraic and analytic techniques and thus might be considered as a bridge between both worlds''. Often inspired by concrete problems from the analysis of algorithms and data structures, powerful analytic combinatorics methods have been developed to describe the asymptotic behaviour of quantities in random structures. In this minisymposium several such recent results will be presented, where generating functions techniques play an essential r\^{o}le. Monday June 10 15:15 - 15:40 Bernhard Gittenberger (Technische UniversitÃ¤t Wien), Associative and commutative tree representations for Boolean functions, Science SN-2101 15:45 - 16:10 Helmut Prodinger (Stellenbosch University), Generating functions in the analysis of $m$-versions of approximate counting, binary search trees and other structures, Science SN-2101 16:15 - 16:40 Alfredo Viola (Universidad de la RepÃºblica), Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields, Science SN-2101 16:45 - 17:10 Mark Daniel Ward (Purdue University), Recent Directions in Tries, Pattern Matching, Suffix Trees, and Subword Complexity, Science SN-2101 17:15 - 17:40 Marie-Louise Bruner (Vienna University of Technology, Austria), Parking in trees, Science SN-2101 Applied Combinatorics and the Natural Sciences I (CM16) Chair: Chris Soteros (University of Saskatchewan) Org: Marni Mishna (Simon Fraser University), Chris Soteros (University of Saskatchewan) and Karen Yeats (Simon Fraser University) The natural sciences provide a rich source of inspiration for discrete mathematics. The proposed minisymposia (2 sessions with 4-5 speakers each) bring together researchers with a common interest in combinatorial modelling of natural phenomena in chemistry, physics and biology. Areas of application include: phase transitions, models of DNA/RNA, and quantum field theory. Combinatorial approaches include: integral and functional equation methods, kernel method, Monte Carlo and random generation schemes. The session speakers reflect a mixture of applied combinatorics expertise: some focussed more on the analytical and computational tools while others focussed more on the applications. This cross-fertilization at the interface between discrete mathematics and the natural sciences will inspire improvements both in the models and in the combinatorial analysis. Wednesday June 12 10:10 - 10:35 Stuart Whittington (University of Toronto, Canada), Partially directed walks and polymer adsorption on striped surfaces, Science SN-2105 10:40 - 11:05 Marni Mishna (Simon Fraser University, Canada), A combinatorial approach to lattice path asymptotics, Science SN-2105 11:10 - 11:35 Aleks Owczarek (University of Melbourne, Australia), Exact solution of two friendly walks above a sticky wall with single and double interactions, Science SN-2105 11:40 - 12:05 Iain Crump (Simon Fraser University, Canada), Forbidden minors and Feynman graphs, Science SN-2105 12:10 - 12:35 Michael Szafron (University of Saskatchewan, Canada), Using self-avoiding polygons to study DNA-Enzyme Interactions, Science SN-2105 Applied Combinatorics and the Natural Sciences II (CM23) Chair: Marni Mishna (Simon Fraser University) Org: Marni Mishna (Simon Fraser University), Chris Soteros (University of Saskatchewan) and Karen Yeats (Simon Fraser University) The natural sciences provide a rich source of inspiration for discrete mathematics. The proposed minisymposia (2 sessions with 4-5 speakers each) bring together researchers with a common interest in combinatorial modelling of natural phenomena in chemistry, physics and biology. Areas of application include: phase transitions, models of DNA/RNA, and quantum field theory. Combinatorial approaches include: integral and functional equation methods, kernel method, Monte Carlo and random generation schemes. The session speakers reflect a mixture of applied combinatorics expertise: some focussed more on the analytical and computational tools while others focussed more on the applications. This cross-fertilization at the interface between discrete mathematics and the natural sciences will inspire improvements both in the models and in the combinatorial analysis. Thursday June 13 10:10 - 10:35 E. J. Janse van Rensburg (York University, Canada), Some results on inhomogeneous percolation, Science SN-2101 10:40 - 11:05 Sophie Burrill (Simon Fraser University, Canada), Using generating trees to construct Skolem sequences, Science SN-2101 11:10 - 11:35 Chris Soteros (University of Saskatchewan, Canada), Combinatorics of the entanglement complexity of stretched polygons in a lattice tube, Science SN-2101 11:40 - 12:05 Tom Boothby (Simon Fraser University), Topological Metrics on Permutations, Science SN-2101 12:10 - 12:35 Karen Yeats (Simon Fraser University, Canada), Using combinatorics to understand Dyson-Schwinger equations, Science SN-2101 Chromatic Graph Theory (CM6) Organizer and Chair: Joan P. Hutchinson (Macalester College, emerita) Coloring graphs has interested practicioners since the beginning of graph theory. Over time a wide variety of approaches has been developed, turning the field into one of continuing interest and connection with other branches of graph theory and its applications. In this mini-symposium we sample a range of topics: edge-coloring and its connections with Hamiltonicity; list-coloring and its uses with graphs on surfaces, planar and nonplanar; and algorithms and complexity of injective and frugal colorings and related homomorphisms. Monday June 10 15:15 - 15:40 Stan Wagon (Macalester College), Computational Hamiltonianism, Science SN-2098 15:45 - 16:10 Gary MacGillivray (University of Victoria), Locally injective homomorphisms, Science SN-2098 16:15 - 16:40 Luke Postle (Emory University), Linear Isoperimetric Bounds in Graph Coloring, Science SN-2098 16:45 - 17:10 Joan Hutchinson (Macalester College), A variation on Heawood-list-coloring for graphs on surfaces, Science SN-2098 Cycle Decompositions of Graphs I (CM12) Chair: Mateja Sajna (University of Ottawa) Org: Andrea Burgess (Ryerson University) and Mateja Sajna (University of Ottawa) In the last 15 years, enormous progress has been made in the area of cycle decompositions of graphs. A breakthrough was made by Alspach, Jordon and \v{S}ajna, who determined necessary and sufficient conditions for the existence of an $m$-cycle decomposition of the complete graph $K_n$. In 2011, this result was extended to complete multigraphs by Bryant, Horsley, Maenhaut, and Smith. Perhaps even more impressive are the 2012 complete solution to the long-outstanding Alspach's conjecture on decomposing complete graphs into cycles of various lengths by Bryant, Horsley, and Pettersson, and the first solution to the Oberwolfach Problem for an infinite set of orders by Bryant and Scharaschkin. Many other results on cycle decompositions of various graphs and with various prescribed properties have been proved during this time. In this 2-part minisymposium, we would like to gather some of the researchers who have contributed most to this flourishing research area. Tuesday June 11 15:15 - 15:40 Darryn Bryant (University of Queensland), Repacking in cycle decompositions., Science SN-2098 15:45 - 16:10 Daniel Horsley (Monash University), Decomposing complete bipartite graphs into short cycles and related results, Science SN-2098 16:15 - 16:40 Barbara Maenhaut (University of Queensland), Cycle decompositions of complete multigraphs, Science SN-2098 16:45 - 17:10 Peter Danziger (Ryerson University), Bipartite 2-factorisations of complete multipartite graphs, Science SN-2098 17:15 - 17:40 Andrea Burgess (Ryerson University), Orthogonally resolvable cycle decompositions, Science SN-2098 Cycle Decompositions of Graphs II (CM17) Chair: Andrea Burgess (Ryerson University) Org: Andrea Burgess (Ryerson University) and Mateja Sajna (University of Ottawa) In the last 15 years, enormous progress has been made in the area of cycle decompositions of graphs. A breakthrough was made by Alspach, Jordon and \v{S}ajna, who determined necessary and sufficient conditions for the existence of an $m$-cycle decomposition of the complete graph $K_n$. In 2011, this result was extended to complete multigraphs by Bryant, Horsley, Maenhaut, and Smith. Perhaps even more impressive are the 2012 complete solution to the long-outstanding Alspach's conjecture on decomposing complete graphs into cycles of various lengths by Bryant, Horsley, and Pettersson, and the first solution to the Oberwolfach Problem for an infinite set of orders by Bryant and Scharaschkin. Many other results on cycle decompositions of various graphs and with various prescribed properties have been proved during this time. In this 2-part minisymposium, we would like to gather some of the researchers who have contributed most to this flourishing research area. Wednesday June 12 10:10 - 10:35 Marco Buratti (UniversitÃ  degli Studi di Perugia), Cycle decompositions and their automorphism groups, Science SN-2098 10:40 - 11:05 Danny Dyer (Memorial University), Graceful Labellings of Triangular Cacti, Science SN-2098 11:10 - 11:35 Heather Jordon (American Mathematical Society), Cycle Decompositions of Complete Graphs and Circulants, Science SN-2098 11:40 - 12:05 Sibel Ozkan (Gebze Institute of Technology), On the Hamilton-Waterloo Problem with uniform cycle sizes, Science SN-2098 12:10 - 12:35 Mateja Sajna (University of Ottawa), On the directed Oberwolfach Problem with equal cycle length, Science SN-2098 Decidability in Automatic and Related Sequences (CM8) Organizer and Chair: Jeffrey Shallit (University of Waterloo) A sequence $(a(n))$ over a finite alphabet is said to be $k$-automatic if there is a deterministic finite automaton that, on input $n$ expressed in base $k \geq 2$, reaches a state with output $a(n)$; a typical example is the classical Thue-Morse sequence. The recent realization that many questions about these sequences can be phrased in the logical theory $(\mathbb{N}, +, <, V_k)$, where $V_k(n)$ is the highest power of $k$ dividing $n$, leads to a decision procedure for answering these questions. In this mini-symposium we will describe this decision procedure and look at some of its many ramifications. Using the decision procedure, we can reprove many results in the literature and find new ones. Although the worst-case running time of the decision procedure is very bad, an implementation often succeeds in mechanically proving the assertions in question. We also address the limitations of the method. Tuesday June 11 10:10 - 10:35 Jeffrey Shallit (University of Waterloo), Decidability in Automatic Sequences, Science SN-2101 10:40 - 11:05 Daniel Goc (University of Waterloo), Automatic Theorem-Proving in Automatic Sequences, Science SN-2101 11:10 - 11:35 Narad Rampersad (University of Winnipeg), Extremal words in the shift orbit closure of a morphic sequence, Science SN-2101 11:40 - 12:05 James Currie (University of Winnipeg), Abelian powers and patterns in words: problems and perspectives, Science SN-2101 12:10 - 12:35 Luke Schaeffer (University of Waterloo), Abelian powers in automatic sequences are not always automatic, Science SN-2101 Discrete Math Coast to Coast: Newfoundland and the West (CM24) Chair: Kseniya Garaschuk (University of Victoria) Org: Gary MacGillivray (University of Victoria) This two-part minisymposium features a speaker from each province, where "from" means was born there, or educated there, or grew up there. One of the goals is for the talks to reflect the richness and diversity of discrete mathematics across Canada. The speakers in this part are "from" Newfoundland, BC, Alberta, Saskatchewan, and Manitoba. Thursday June 13 10:10 - 10:35 Kathleen Barnetson (Memorial University of Newfoundland), Searching for Class Uniformly Resolvable Partial Coverings, Arts A-1046 10:40 - 11:05 Kseniya Garaschuk (University of Victoria), Fractional decompositions of dense graphs, Arts A-1046 11:10 - 11:35 Bill Sands (University of Calgary), Covering with intervals in distributive lattices, Arts A-1046 11:40 - 12:05 Karen Meagher (University of Regina), Minimum number of distinct eigenvalues of a graph, Arts A-1046 12:10 - 12:35 Shonda Gosselin (University of Winnipeg), Algebraic hypergraph decompositions, Arts A-1046 Discrete Math Coast to Coast: The Maritimes and the Middle (CM27) Chair: Chris Duffy (University of Victoria) Org: Gary MacGillivray (University of Victoria) This two-part minisymposium features a speaker from each province, where "from" means was born there, or educated there, or grew up there. One of the goals is for the talks to reflect the richness and diversity of discrete mathematics across Canada. The speakers in this part are "from" New Brunswich, Nova Scotia, PEI, Quebec and Ontario. Thursday June 13 15:15 - 15:40 Nancy Clarke (Acadia University), Oriented Injective Colouring, Arts A-1046 15:45 - 16:10 Shannon Fitzpatrick (University of Prince Edward Island), Grundy Number and the Strong Product, Arts A-1046 16:15 - 16:40 Ben Seamone (Universite de Montreal), Some results on strong edge colourings, Arts A-1046 16:45 - 17:10 Margaret-Ellen Messinger (Mount Allison University), The Cop Number and Tree Decompositions, Arts A-1046 17:15 - 17:40 Chris Duffy (University of Victoria), Game Show Scheduling and Orderings of Elements of a Product, Arts A-1046 Domination in Graphs (CM13) Organizer and Chair: Gary MacGillivray (University of Victoria) Domination is one of the most studied topics in graph theory. The goal of this minisymposuim is to string together five talks on recent progress in different aspects of this broad area. Tuesday June 11 15:15 - 15:40 Stephen Finbow (St. Francis Xavier), Equality in the Domination Chain in Planar Triangulisations, Science SN-2101 15:45 - 16:10 Ortrud Oellermann (University of Winnipeg), Domination and Digital Convexity Parameters, Science SN-2101 16:15 - 16:40 Rick Brewster (Thompson Rivers University), Broadcast domination and its dual multipackings, Science SN-2101 16:45 - 17:10 Michelle Edwards (University of Victoria), Independent Domination Bicritical Graphs, Science SN-2101 17:15 - 17:40 Ruth Haas (Smith College), The k-dominating graph, Science SN-2101 Eric Mendelsohn: Colleagues and Descendants I (CM1) Chair: Brett Stevens (Carleton University) Org: Peter Danziger (Ryerson University) and Brett Stevens (Carleton University) These minisymposia celebrate the influence and work of Eric Mendelsohn through his collaborators, students, and other colleagues. At age 1, Eric Mendelsohn was a registered participant at the inaugural 1945 Montreal meeting of the Canadian Mathematics Society. His activities and influence in discrete mathematics continue to this day. He was hired at the Department of Mathematics at the University of Toronto in 1970, where he has been full professor since 1982. He retired from the University in 2010, and is now professor emeritus. He is currently an adjunct professor with the department of Mathematics at Ryerson University, whose support we gratefully acknowledge. Eric has 94 publications, 55 co-authors, 13 official "descendants". He has been an important force in combinatorics and discrete mathematics over many years, his energy and vision have provided many important directions and insights. Monday June 10 10:10 - 10:35 Jason Brown (Dalhousie University), Colourful problems in combinatorics, Arts A-1046 10:40 - 11:05 Nevena Francetic (Carleton University), Relation between optimal group divisible packing and covering designs, Arts A-1046 11:10 - 11:35 Douglas Stinson (University of Waterloo), Combinatorial Aspects of Key Distribution for Sensor Networks, Arts A-1046 11:40 - 12:05 Karen Meagher (University of Regina), Covering arrays on graphs, Arts A-1046 Eric Mendelsohn: Colleagues and Descendants II (CM7) Chair: Brett Stevens (Carleton University) Org: Peter Danziger (Ryerson University) and Brett Stevens (Carleton University) These minisymposia celebrate the influence and work of Eric Mendelsohn through his collaborators, students, and other colleagues. At age 1, Eric Mendelsohn was a registered participant at the inaugural 1945 Montreal meeting of the Canadian Mathematics Society. His activities and influence in discrete mathematics continue to this day. He was hired at the Department of Mathematics at the University of Toronto in 1970, where he has been full professor since 1982. He retired from the University in 2010, and is now professor emeritus. He is currently an adjunct professor with the department of Mathematics at Ryerson University, whose support we gratefully acknowledge. Eric has 94 publications, 55 co-authors, 13 official "descendants". He has been an important force in combinatorics and discrete mathematics over many years, his energy and vision have provided many important directions and insights. Monday June 10 15:15 - 15:40 Robert Bailey (Ryerson University), Generalized packing designs with block size 5, Arts A-1046 15:45 - 16:10 Derek Corneil (University of Toronto), Graph searches and cocomparability graphs, Arts A-1046 16:15 - 16:40 Peter Dukes (University of Victoria), Designs of high dimension, Arts A-1046 16:45 - 17:10 Nabil Shalaby (Memorial University of Newfoundland), Skolem labelled graphs, old and new results, Arts A-1046 Eric Mendelsohn: Colleagues and Descendants III (CM9) Chair: Peter Danziger (Ryerson University) Org: Peter Danziger (Ryerson University) and Brett Stevens (Carleton University) These minisymposia celebrate the influence and work of Eric Mendelsohn through his collaborators, students, and other colleagues. At age 1, Eric Mendelsohn was a registered participant at the inaugural 1945 Montreal meeting of the Canadian Mathematics Society. His activities and influence in discrete mathematics continue to this day. He was hired at the Department of Mathematics at the University of Toronto in 1970, where he has been full professor since 1982. He retired from the University in 2010, and is now professor emeritus. He is currently an adjunct professor with the department of Mathematics at Ryerson University, whose support we gratefully acknowledge. Eric has 94 publications, 55 co-authors, 13 official "descendants". He has been an important force in combinatorics and discrete mathematics over many years, his energy and vision have provided many important directions and insights. Tuesday June 11 10:10 - 10:35 Aiden Bruen (Carleton University), Unimbeddable nets of small deficiency, Arts A-1046 10:40 - 11:05 Frantisek Franek (McMaster University), On the singularities of extremal periodic strings, Arts A-1046 11:10 - 11:35 Sebastian Raaphorst (University of Ottawa), The Lovasz Local Lemma and Variable Strength Covering Arrays, Arts A-1046 11:40 - 12:05 Ben Seamone (University de Montreal), Bounding a graph's weight choosability number, Arts A-1046 12:10 - 12:35 Daniela Silvesan (Memorial University of Newfoundland), Cyclic, Simple and Indecomposable Three-Fold Triple Systems, Arts A-1046 Finite Fields in Combinatorics I (CM14) Chair: David Thomson (Carleton University) Org: Petr Lisonek (Simon Fraser University) and David Thomson (Carleton University) The areas of finite fields and combinatorics are strongly linked. The talks in this minisymposium highlight the versatility in the use of finite fields to construct interesting classes of combinatorial objects and prove results about them. Topics addressed in the talks include error control codes, finite geometries, planar functions, Costas and related arrays, sequences with good correlation properties, permutation polynomials, decomposition of polynomials, and more. Tuesday June 11 15:15 - 15:40 Aiden Bruen (Carleton University), Dickson's theorem: applications and generalizations, Arts A-1046 15:45 - 16:10 Yue Zhou (Otto-von-Guericke University of Magdeburg), Planar functions over finite fields with characteristic two, Arts A-1046 16:15 - 16:40 Petr Lisonek (Simon Fraser University), Construction X for quantum error-correcting codes, Arts A-1046 16:45 - 17:10 Kenza Guenda (University of Victoria), The equivalency problem for cyclic combinatorial objects, Arts A-1046 17:15 - 17:40 Jane Wodlinger (University of Victoria), Structural properties of Costas arrays, Arts A-1046 Finite Fields in Combinatorics II (CM18) Chair: Petr Lisonek (Simon Fraser University) Org: Petr Lisonek (Simon Fraser University) and David Thomson (Carleton University) The areas of finite fields and combinatorics are strongly linked. The talks in this minisymposium highlight the versatility in the use of finite fields to construct interesting classes of combinatorial objects and prove results about them. Topics addressed in the talks include error control codes, finite geometries, planar functions, Costas and related arrays, sequences with good correlation properties, permutation polynomials, decomposition of polynomials, and more. Wednesday June 12 10:10 - 10:35 Daniel Katz (California State University, Northridge), Weil Sums of Binomials with Three-Valued Spectra, Arts A-1046 10:40 - 11:05 Jing He (Carleton University), A new class of almost perfect sequences and a new family of Zero Correlation Zone sequences, Arts A-1046 11:10 - 11:35 Xiang-dong Hou (University of South Florida), A Class of Permutation Binomials over Finite Fields, Arts A-1046 11:40 - 12:05 Mark Giesbrecht (University of Waterloo), Decomposition of additive polynomials and matrix similarity classes, Arts A-1046 12:10 - 12:35 David Thomson (Carleton University), On a conjecture of Golomb and Moreno, Arts A-1046 Galois Geometries and Applications I (CM20) Chair: Jan De Beule (Ghent University) Org: Jan De Beule (Ghent University) and Petr Lisonek (Simon Fraser University) Galois geometries is the research field in which projective spaces over the finite fields, also called Galois fields, are investigated. This includes the study of their substructures and their links to other research areas. Many of these substructures are investigated for their geometrical importance, such as the quadrics and the Hermitian varieties, but many substructures are investigated because of their links to other research areas such as coding theory. This includes the link between arcs in Galois geometries and linear MDS codes. Recently, also links between random network coding and Galois geometries have been found. The techniques used in Galois geometries involve, next to geometrical techniques, also other techniques such as the polynomial method. This minisymposium will discuss different aspects of Galois geometries. This includes theoretical results and links to coding theory. Wednesday June 12 15:15 - 15:40 Peter Sziklai (Eotvos Lorand University, Budapest, Hungary), The direction problem: old and new results, Science SN-2105 15:45 - 16:10 Qing Xiang (University of Delaware, USA), Constructions of difference sets and strongly regular graphs using cyclotomic classes, Science SN-2105 16:15 - 16:40 Brett Stevens (Carleton University, Canada), Linear feedback shift registers and covering arrays, Science SN-2105 16:45 - 17:10 Petr Lisonek (Simon Fraser University, Canada), Quantum codes from generalized quadrangles, Science SN-2105 17:15 - 17:40 Kathryn Haymaker (University of Nebraska - Lincoln, USA), Write once memory codes from finite geometries, Science SN-2105 Galois Geometries and Applications II (CM25) Chair: Petr Lisonek (Simon Fraser University) Org: Jan De Beule (Ghent University) and Petr Lisonek (Simon Fraser University) Galois geometries is the research field in which projective spaces over the finite fields, also called Galois fields, are investigated. This includes the study of their substructures and their links to other research areas. Many of these substructures are investigated for their geometrical importance, such as the quadrics and the Hermitian varieties, but many substructures are investigated because of their links to other research areas such as coding theory. This includes the link between arcs in Galois geometries and linear MDS codes. Recently, also links between random network coding and Galois geometries have been found. The techniques used in Galois geometries involve, next to geometrical techniques, also other techniques such as the polynomial method. This minisymposium will discuss different aspects of Galois geometries. This includes theoretical results and links to coding theory. Thursday June 13 10:10 - 10:35 Alfred Wassermann (University of Bayreuth, Germany), Construction of $q$-analogs of Steiner systems, Science SN-2105 10:40 - 11:05 Michael Braun (University of Darmstadt, Germany), $q$-Analog of Packing Designs, Science SN-2105 11:10 - 11:35 Maarten De Boeck (Ghent University, Belgium), The Erd\H{o}s-Ko-Rado problem for geometries, Science SN-2105 11:40 - 12:05 Sara Rottey (VUB (Vrije Universiteit Brussel), Belgium), The automorphism group of linear representations, Science SN-2105 12:10 - 12:35 Jan De Beule (Ghent University, Belgium), Constructing Cameron-Liebler line classes with large parameter, Science SN-2105 Geometric Representations of Graphs (CM10) Organizer and Chair: Steven Chaplick (Charles University, Prague, Czech Republic) Visualizations and representations of graphs by means of intersections or contacts of geometric objects have been widely investigated. Classical examples are interval graphs and Koebe circle representations. When representations are given they can sometimes be exploited in optimization problems. In many instances these problems are hard for general graphs but become polynomial-time solvable when restricted to intersection or contact graphs with a given representations. Another class of problems is to compute the representation or to decide whether it exists. In this minisymposium we highlight some recent developments in this active area at the intersection of graph theory and discrete geometry. Tuesday June 11 10:10 - 10:35 Steven Chaplick (Charles University, Prague, Czech Republic), Max Point-Tolerance Graphs, Science SN-2105 10:40 - 11:05 Anna Lubiw (University of Waterloo, Waterloo, Canada), Morphing Planar Graph Drawings, Science SN-2105 11:10 - 11:35 Marcus Schaefer (DePaul University, Chicago, U.S.A.), Toward a Theory of Planarity: An algorithm for simultaneous planarity?, Science SN-2105 11:40 - 12:05 Torsten Ueckerdt (Karlsruhe Institute of Technology, Karlsruhe, Germany), Various Applications of L, Science SN-2105 12:10 - 12:35 Ryuhei Uehara (Japan Advanced Institute of Science and Technology, Nomi, Japan), The graph isomorphism problem on graphs with geometric representations, Science SN-2105 Graph Homomorphisms (CM2) Organizer and Chair: Pavol Hell (SFU) The speakers will focus on recent results concerning various aspects of graph homomorphisms Monday June 10 10:10 - 10:35 Laszlo Egri (Hungarian Academy of Sciences, Budapest), List H-Coloring a Graph by Removing Few Vertices, Science SN-2098 10:40 - 11:05 Robert Samal (Charles University, Prague), Hedetniemi conjecture for strict vector chromatic number, Science SN-2098 11:10 - 11:35 Hamed Hatami (McGill University, Montreal), The entropy of random-free graphons and properties, Science SN-2098 11:40 - 12:05 Jaroslav Nesetril (Charles University, Prague), Tree-depth primer, Science SN-2098 12:10 - 12:35 Patrice Ossona de Mendez (L'Ecole des Hautes Etudes en Sciences Sociales, Paris), A first Intermediate class with limit object, Science SN-2098 Graph Structure and Algorithms (CM3) Organizer and Chair: Kathie Cameron (Wilfrid Laurier University) Often graphs arising in applications have special structure. This structure can sometimes be used to design efficient algorithms for problems that are hard in general. Clearly, special structure is needed to prove the existence of certain types of subgraphs which do not exist in more general graphs. In this minisymposium, we see four instances of efficient algorithms and existence theorems which exploit special structure, and one anomalous algorithmic problem which was solved by ignoring the special graph structure. Monday June 10 10:10 - 10:35 Jessica Enright (University of Glasgow), On List Colouring and List Homomorphism of Permutation and Interval Graphs, Science SN-2105 10:40 - 11:05 Elaine Eschen (West Virginia University), Colored Graph Completion, Science SN-2105 11:10 - 11:35 R. Sritharan (University of Dayton), Hendry's conjecture holds for spider intersection graphs, Science SN-2105 11:40 - 12:05 Kathie Cameron (Wilfrid Laurier University), Same-Degree Trees and Intermediate Trees, Science SN-2105 12:10 - 12:35 Katie Tsuji (University of Waterloo), Finding Monotone Path Systems in Regions with Holes, Science SN-2105 Graph Theory with Applications in Chemistry I (CM19) Chair: Patrick Fowler (University of Sheffield) Org: Patrick Fowler (University of Sheffield) and Wendy Myrvold (University of Victoria) This session and the following linked session explore applications of graph theory to chemistry. Part I includes contributions on graph theory with applications to currents in molecules. Ballistic currents driven through molecules in an electric circuit and ring current circulations generated within aromatic molecules by a magnetic field are both of importance in chemistry and materials science, and both can be modelled using techniques from spectral graph theory and the theory of perfect matchings. Speakers will discuss some of these models and the connections between them. Wednesday June 12 10:10 - 10:35 Patrick W Fowler (University of Sheffield), Conjugated circuits, currents in benzenoids and equiaromaticity, Science SN-2101 10:40 - 11:05 Wendy Myrvold (University of Victoria), Models of Current Density Maps of Benzenoids, Science SN-2101 11:10 - 11:35 Matthias Ernzerhof (University of Montreal), The zero-voltage conductance of nano-graphenes: Simple rules and, Science SN-2101 11:40 - 12:05 Irene Sciriha (University of Malta), Molecular Graphs with Analogous Conducting Connections, Science SN-2101 12:10 - 12:35 Barry T Pickup (University of Sheffield), Effects of Pauli blockade on single-molecule conduction, Science SN-2101 Graph Theory with Applications in Chemistry II (CM21) Chair: Wendy Myrvold (University of Victoria) Org: Patrick Fowler (University of Sheffield) and Wendy Myrvold (University of Victoria) This session and the previous linked session explore applications of graph theory to chemistry. Part II includes contributions on graph theory with applications to molecular structure, stability and reactivity. Stability and properties of fullerenes and benzenoids are of theoretical and practical interest in chemistry, and are often modelled using theories based on perfect matchings and graph spectra. Talks will include discussion of two models of fullerene (and benzenoid) stability based on the ideas proposed by Clar and Fries, extension of graph spectral models to saturated systems, and new models of chemical reactivity. Wednesday June 12 15:15 - 15:40 Elizabeth Hartung (Massachusetts College of Liberal Arts), The Clar Structures of a Fullerene, Science SN-2101 15:45 - 16:10 Jack E Graver (Syracuse University), The Fries Structures of a fullerene, Science SN-2101 16:15 - 16:40 Craig E Larson (Virginia Commonwealth University), Eigenvalues of Saturated Hydrocarbons, Science SN-2101 16:45 - 17:10 Nico Van Cleemput (University of Gent), Spherical Tilings by Congruent Quadrangles, Science SN-2101 17:15 - 17:40 Douglas J Klein (Texas A&M University at Galveston), Substitution-reaction posets in chemistry, Science SN-2101 Gray Codes and Universal Cycles (CM15) Chair: Joe Sawada (University of Guelph) Org: Joe Sawada (University of Guelph) and Aaron Williams (McGill University) The ability to efficiently generate all possible instances of a particular combinatorial object (permutations, combinations, trees, necklaces, etc) is of practical importance to many areas of scientific research. It is the primary topic in Knuth's most recent addition to his series The Art Of Computer Programming''. This session will focus on several key aspects in this area including: (Greedy) Gray codes, Universal cycles, Random generation. In particular, attendees may learn simple ways to construct their family tree'' and how to greedily flip pancakes''. Tuesday June 11 15:15 - 15:40 Joe Sawada (University of Guelph), An overview of Combinatorial Generation, Science SN-2105 15:45 - 16:10 Aaron Williams (McGill University), Iterative Gray Codes, Science SN-2105 16:15 - 16:40 Ryuhei Uehara (Japan Advanced Institute of Science and Technology), On generation of graphs with geometric representations, Science SN-2105 16:45 - 17:10 Xi Sisi Shen (McGill University), A "Hot Potato" transposition Gray code for permutations, Science SN-2105 Hypergraphs (CM22) Chair: Amin Bahmanian (University of Ottawa) Org: Amin Bahmanian and Mateja Sajna (University of Ottawa) In the last decade, hypergraph theory has emerged as a powerful mathematical tool in a variety of real-life applications. However, in spite of its remarkable developments, the theory of hypergraphs has not yet given rise to extensive literature comparing to the theory of graphs. For example, very little is known about edge decompositions of hypergraphs, even for special cases. Perhaps the best evidence for the difficulty of questions about hypergraphs is Sylvester's Problem, which asks about the existence of a 1-factorization of the complete uniform hypergraph. It took 120 years before Baranyai finally solved this problem. The goal of this minisymposium is to bring together experts in various areas of hypergraph theory. The main areas of interest are edge colorings, edge decompositions, amalgamations, detachments, and embeddings. Wednesday June 12 15:15 - 15:40 Shonda Gosselin (University of Winnipeg), Cyclic decompositions of complete and complete multipartite uniform hypergraphs, Science SN-2098 15:45 - 16:10 Andrzej Czygrinow (Arizona State University), Loose cycles in 3-uniform hypergraphs, Science SN-2098 16:15 - 16:40 Amin Bahmanian (University of Ottawa), 2-edge-connected fair detachments of $(\leq 3)$-graphs, Science SN-2098 16:45 - 17:10 Imdadullah Khan (Umm Al Qura University), Perfect matchings in uniform hypergraph with large vertex degree, Science SN-2098 17:15 - 17:40 Mateja Sajna (University of Ottawa), Eulerian-type properties of hypergraphs, Science SN-2098 Independence Number: Theory and Applications I. (CM26) Chair: Craig Larson (Virginia Commonwealth University) Org: Ermelinda DeLaVina (University of Houston--Downtown) and Craig Larson (Virginia Commonwealth University) Researchers will present recent work related to the independence structure of a graph. Several speakers discuss advances in the investigation of well-covered graphs, graphs where every maximal independent set is a maximum independent set. Other research includes new bounds for the independence number, new bounds for the number of independent structures, and theory and problems related to the efficient computation of the independence number. Thursday June 13 10:10 - 10:35 Michael D. Plummer (Vanderbilt University), A Problem On Well-covered Graphs, Science SN-2098 10:40 - 11:05 Art Finbow (Saint Mary's University), On Well-Covered Planar Triangulations, Science SN-2098 11:10 - 11:35 William Staton (University of Mississippi), Independence Polynomials of k-Trees, Science SN-2098 11:40 - 12:05 David Tankus (Ariel University of Samaria), Weighted Well-Covered Graphs without Cycles of Lengths 4, 5, and 6, Science SN-2098 12:10 - 12:35 Ermelinda DeLaVina (University of Houston--Downtown), Graffiti.pc on Independence, Science SN-2098 Independence Number: Theory and Applications II. (CM28) Chair: Ermelinda DeLaVina (University of Houston--Downtown) Org: Ermelinda DeLaVina (University of Houston--Downtown) and Craig Larson (Virginia Commonwealth University) Researchers will present recent work related to the independence structure of a graph. Several speakers discuss advances in the investigation of well-covered graphs, graphs where every maximal independent set is a maximum independent set. Other research includes new bounds for the independence number, new bounds for the number of independent structures, and theory and problems related to the efficient computation of the independence number. Thursday June 13 15:15 - 15:40 Doug Rall (Furman University), On Maximal Independent Sets in Cartesian Products, Science SN-2098 15:45 - 16:10 Bert Hartnell (Saint Mary's University), Eternal Domination with Independent Guards, Science SN-2098 16:15 - 16:40 Jochen Harant (Ilmenau University of Technology), Packing of isomorphic induced independent subgraphs, Science SN-2098 16:45 - 17:10 Craig Larson (Virginia Commonwealth University), The Independence Number Project, Science SN-2098 17:15 - 17:40 Ryan Pepper (University of Houston--Downtown), Recent Results on k-independence in graphs, Science SN-2098 Nested Recurrence Relations (CM4) Organizer and Chair: Frank Ruskey (University of Victoria) Hofstadter introduced the recurrence $Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2))$, an example of a \textit{nested recurrence relation} (or NRR) because it has a sub-expression of the form $â€¦Q(â€¦Q(â€¦)â€¦)â€¦$. Other than composition, the only operations that are used are addition/subtraction. Recently there has been a flurry of activity in trying to understand and solve'' NRRs. Some NRRs have a solution and combinatorial interpretations, while others seemingly do not. It is still unknown whether $Q(n)$ is defined for all $n$. On the other hand, the recurrence $T(n)=T(n-1-T(n-1))+T(n-2-T(n-2))$ with $T(1)=T(2)=T(3)=1$, the number $T(n)$ counts the maximum number of leaves at the lowest level in a $n$-node binary tree. There are many recent results that show that NRRs arise from natural counting problems in certain classes of highly structured infinite trees. There are undecidable NRRs and some that are related to automatic sequences. This minisymposium will introduce NRRs, present some recent results, and offer tantalizing open problems. Monday June 10 10:10 - 10:35 Steve Tanny (University of Toronto), An Invitation to Nested Recurrence Relations, Science SN-2101 10:40 - 11:05 Mustazee Rahman (University of Toronto), Nested Recursions, Simultaneous Parameters and Tree Superpositions, Science SN-2101 11:10 - 11:35 Jeff Shallit (University of Waterloo), Automata and nested recurrences, Science SN-2101 11:40 - 12:05 Marcel Celaya (McGill University), Morphic Words and Nested Recurrence Relations, Science SN-2101 12:10 - 12:35 Frank Ruskey (University of Victoria), An undecidable nested recurrence relation, Science SN-2101 Partitioning Graphs into Independent Sets and Cliques (CM11) Organizer and Chair: Dennis D.A. Epple (University of Victoria) A natural generalization of graph colourings is to consider partitions of the vertex set of graphs into independent sets and cliques. This idea gives rise to a wide field of topics including $(k,l)$-colourings, split graphs, the cochromatic number, and matrix partitions. This minisymposium features a broad selection of current research in the area. Tuesday June 11 10:10 - 10:35 Dennis D.A. Epple (University of Victoria), Young diagrams for $(k,l)$-colourings, Science SN-2098 10:40 - 11:05 TÄ±naz Ekim (BoÄŸaziÃ§i University), Defective Cocolorings, Science SN-2098 11:10 - 11:35 Juraj Stacho (University of Warwick), Stable-$\Pi$ partitions of graphs, Science SN-2098 11:40 - 12:05 Pavol Hell (Simon Fraser University), Matrix partitions, Science SN-2098 12:10 - 12:35 Mayssam Mohammadi Nevisi (Simon Fraser University), Counting Partitions of Graphs, Science SN-2098