CanaDAM 2015 University of Saskatchewan, June 1 - 4, 2015 www.cms.math.ca//2015
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# Contributed Minisymposia

There will be contributed minisymposia in the following areas.

Algorithmic construction of combinatorial objects
Organizer and Chair: Jan Goedgebeur (Ghent University)

Computers are often used in combinatorics to determine if combinatorial objects with given structural or extremal properties exist as these existence problems are often too complex to solve by hand. This is done by designing and implementing generation algorithms which construct combinatorial objects from a given class (typically avoiding the generation of isomorphic copies). In this minisymposium we will give an overview of specialized generation algorithms which have been applied to solve various combinatorial problems.

Geoffrey Exoo (Indiana State University), Jan Goedgebeur (Ghent University), Veronika Irvine (University of Victoria), Stanislaw Radziszowski (Rochester Institute of Technology), Aaron Williams (Bard College at Simon's Rock).

Automated analysis of combinatorial structures
Organizer and Chair: Stephen Melczer (University of Waterloo and ENS Lyon)

Over the last several decades, techniques coming from pure mathematics, computer science, combinatorics, and probability theory have been combined in novel ways to permit automatic yet rigorous analysis of combinatorial structures and their underlying properties. This minisymposium will give a broad view of these approaches, including talks on the theoretical tools developed for this purpose — such as Analytic Combinatorics in Several Variables — along with recent applications to the study of lattice walks and polymer models. By combining both theory and practice, the session aims to strengthen old collaborations and foster new ones.

Torin Greenwood (University of Pennsylvania), Hui Huang (RISC - Linz), Marni Mishna (Simon Fraser University), Mark Wilson (University of Auckland), Thomas Wong (University of British Columbia).

Colourings, colour graphs, and homomorphisms
Organizer and Chair: Gary MacGillivray (University of Victoria)

This collection of talks begins by discussing when it is possible to generate all $k$-colourings of a complete multipartite graph in minimal change order, that is, when the graph of vertex colourings has a Hamilton cycle. The next topic to be discussed is the structure of graphs which are the graph of the vertex colourings of some other graph. We then move on to connectivity questions for the graph of circular colourings. The final two talks in the minisymposium address colourings of mixed graphs, that is, graphs with several edge sets and several arc sets, and homomorphisms of oriented graphs.

Stefan Bard (University of Victoria), Richard Brewster (Thompson Rivers University), Christopher Duffy (University of Victoria), Gary MacGillivray (University of Victoria).

Combinatorics, topology and statistical mechanics of polymer models I
Organizer and Chair: Nicholas Beaton (University of Saskatchewan) and Andrew Rechnitzer (University of British Columbia)

This series of minisymposia will bring together researchers from a variety of fields, including combinatorics, topological knot theory and statistical mechanics, to discuss models of polymers such as DNA. This range of different perspectives and techniques has led a number of recent developments, and we hope that these sessions will foster further collaborations.

Javier Arsuaga (University of California, Davis), Gerasim Iliev (University of Toronto), EJ Janse van Rensburg (York University), Aleks Owczarek (University of Melbourne), Eric Rawdon (University of St. Thomas).

Combinatorics, topology and statistical mechanics of polymer models II
Organizer and Chair: Nicholas Beaton (University of Saskatchewan) and Andrew Rechnitzer (University of British Columbia)

This series of minisymposia will bring together researchers from a variety of fields, including combinatorics, topological knot theory and statistical mechanics, to discuss models of polymers such as DNA. This range of different perspectives and techniques has led a number of recent developments, and we hope that these sessions will foster further collaborations.

Mahshid Atapour (University of Saskatchewan), Nathan Clisby (University of Melbourne), Neal Madras (York University), Steve Melczer (University of Waterloo), Koya Shimokawa (Saitama University).

Combinatorics, topology and statistical mechanics of polymer models III
Organizer and Chair: Nicholas Beaton (University of Saskatchewan) and Andrew Rechnitzer (University of British Columbia)

This series of minisymposia will bring together researchers from a variety of fields, including combinatorics, topological knot theory and statistical mechanics, to discuss models of polymers such as DNA. This range of different perspectives and techniques has led a number of recent developments, and we hope that these sessions will foster further collaborations.

Nicholas Beaton (University of Saskatchewan), Richard Brak (University of Melbourne), Greg Buck (Saint Anselm College), Jason Cantarella (University of Georgia), Tetsuo Deguchi (Ochanomizu University).

Cycles in graphs I
Organizer and Chair: David Gunderson (University of Manitoba) and Ortrud Oellermann (University of Winnipeg)

Dedicated to the memory of Ralph Faudree. Bondy’s meta conjecture states that almost any condition that guarantees that a graph is Hamiltonian guarantees much more about its cycle structure. In this context, a conjecture of Hendry states that hamiltonian chordal graphs are cycle extendable, i.e., for every non-spanning cycle $C$ there is a cycle $C’$ that contains the vertices of $C$ and one additional vertex. It's shown that this conjecture is false and interesting related results and new directions will be discussed. Ryjáček conjectured that locally connected graphs are weakly pancyclic, i.e., have a cycle of every length between their girth and circumference. Results supporting this conjecture for graphs with certain local conditions are presented and several open problems discussed. For graphs whose cycle spectrum is not continuous, structural properties are obtained; specifically if a given odd cycle length is forbidden and the graph has a maximum number of cycles.

David Brown (Utah State University), David Gunderson (University of Manitoba), Ortrud Oellermann (University of Winnipeg), Ben Seamone (Dawson College), Sergei Tsaturian (University of Manitoba).

Cycles in graphs II
Organizer and Chair: David Gunderson (University of Manitoba) and Ortrud Oellermann (University of Winnipeg)

Dedicated to the memory of Ralph Faudree. This session is devoted to properties of graphs with a large number of cycles. In particular a conjecture of Lovász and Plummer, which states that every 4-connected plane triangulation has a spanning Halin substructure, is shown to be false and properties of plane triangulations that have such substructures are discussed. Matching extension behaviour for families of graphs that are more general than plane triangulations are discussed and results for plane triangulations are compared with results for these more general structures. Graphs and hypergraphs defined using algebraic structures frequently have cyclic decompositions induced by the algebraic structure. Groups and graphs for which the colour-preserving or colour-permuting graph automorphisms all come from the group structure are discussed. Algebraic methods for constructing hypergraph decompositions related to the Payley graph constructions are presented.

Arthur S. Finbow (Saint Marys University), Shonda Gosselin (University of Winnipeg), Joy Morris (Lethbridge University), Michael Plummer (Vanderbilt University).

Extremal combinatorics
Organizer and Chair: Deryk Osthus (University of Birmingham)

Extremal Combinatorics is a vibrant area of Discrete Mathematics. Classical questions in Extremal Combinatorics often can be phrased in the following way: how does some (global) parameter force some (local) structure? An increasingly important trend in the area has been the use of probabilistic techniques and viewpoints. This approach has recently led to a number of major advances. The talks in this minisymposium will reflect this trend.

Roman Glebov (ETH Zurich), Deryk Osthus (University of Birmingham), Guillem Perarnau (McGill), Yury Person (University of Frankfurt), Diana Piguet (Czech Academy of Sciences).

Geometric representations of graphs
Organizer and Chair: Steven Chaplick (TU Berlin)

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 or to obtain deep structural results. For example, in many instances optimization 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.

Steven Chaplick (TU Berlin), Grzegorz Gutowski (Jagiellonian University), Jan Hubicka (University of Calgary), George Mertzios (Durham University).

Graph packings and colorings
Organizer and Chair: Daniel Kral (University of Warwick) and Bojan Mohar (Simon Fraser University)

Graph coloring problems are among the oldest problems in graph theory. The Four Color Theorem is one the most popular graph theory result known to the general public. Graph colorings appear in different scenarios and there have been many extensions of the classical notion of graph coloring proposed. More generally, it is possible to consider graph packings, i.e. partitioning graphs into subgraphs of a certain type. The aim of this minisymposium is to present several recent interesting results from this classical area of graph theory.

Ross Churchley (Simon Fraser University), Ping Hu (University of Warwick), Ross Kang (Radboud University Nijmegen), Robert Samal (Charles University in Prague), Hehui Wu (University of Mississippi).

Graph structure and algorithms
Organizer and Chair: Kathie Cameron (Wilfrid Laurier University)

Often graphs arising in applications have special structure, which can sometimes be exploited to design efficient algorithms for problems that are hard in general. In this minisymposium we look at graph structure that results from excluding certain induced paths, cycles or small graphs, and instances where this allows for efficient algorithms for problems such as colouring and domination.

Kathie Cameron (Wilfrid Laurier University), Murilo da Silva (Simon Fraser University), Elaine Eschen (West Virginia University), Shenwei Huang (Simon Fraser University), Jerry Spinrad (Vanderbilt University).

Graph theory of Brian Alspach I
Organizer and Chair: Joy Morris (University of Lethbridge) and Mateja Sajna (University of Ottawa)

This minisymposium has been organised in honour of Brian Alspach. In person and through his work, Brian has been a major influence on the development of graph theory research in Canada. Since his retirement to Australia, his North American colleagues see him much less often than formerly. We welcome the opportunity of his attendance at this CanaDAM conference to share some of the research of his colleagues, collaborators, and former students, in areas of interest to him, including: Hamilton cycles, groups acting on graphs, tournaments, and cycle decompositions.

Brian Alspach (University of Newcastle), Luis Goddyn (Simon Fraser University), Barbara Maenhaut (University of Queensland), Mateja Sajna (University of Ottawa).

Graph theory of Brian Alspach II
Organizer and Chair: Joy Morris (University of Lethbridge) and Mateja Sajna (University of Ottawa)

This minisymposium has been organised in honour of Brian Alspach. In person and through his work, Brian has been a major influence on the development of graph theory research in Canada. Since his retirement to Australia, his North American colleagues see him much less often than formerly. We welcome the opportunity of his attendance at this CanaDAM conference to share some of the research of his colleagues, collaborators, and former students, in areas of interest to him, including: Hamilton cycles, groups acting on graphs, tournaments, and cycle decompositions.

Klavdija Kutnar (University of Primorska, Slovenia), Dragan Marusic (University of Primorska, Slovenia), Dave Morris (University of Lethbridge), Joy Morris (University of Lethbridge).

Graph theory with applications in chemistry
Organizer and Chair: Patrick Fowler (University of Sheffield) and Wendy Myrvold (University of Victoria)

Stability, structure and properties of carbon networks such as fullerenes and benzenoids are of theoretical and practical interest in chemistry and are often modelled using theories based on perfect matchings, graph adjacency matrices and graph spectra.This session explores ongoing applications of graph theory to carbon chemistry and physics. It includes contributions on models of benzenoid (and fullerene) stability based on the ideas proposed by Clar and Fries, on the construction and classification of carbon nanostructures, on the modelling of the currents induced in carbon structures by external magnetic fields (the ring currents used experimentally to characterise aromatic systems) and on their connections with the concepts of bond order introduced by Coulson and Pauling, both of which are essentially graph theoretical in nature.

Gunnar Brinkmann (University of Gent), Patrick Fowler (University of Sheffield), Jack Graver (University of Syracuse), Elizabeth Hartung (Massachusetts College of Liberal Arts), Wendy Myrvold (University of Victoria).

Graphs and matrices
Organizer and Chair: Shaun Fallat and Karen Meagher (University of Regina)

The study of graphs and matrices lies naturally at the intersection of linear algebra and combinatorics. The interplay of these two different areas has brought new revelations to each field. Often linear algebraic techniques provides insight into combinatorial constructions, objects, and patterns. Conversely, reasoning in combinatorics frequently sheds new light on properties of matrices. In this session, we will have speakers address how these two fields impact each other, present their new findings in these areas and introduce open problems.

Wayne Barrett (Brigham Young University), Jane Breen (University of Manitoba), Karen Meagher (University of Regina).

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