CanaDAM 2017
Université Ryerson, 12 - 16 juin 2017

Graphs and Games: the Mathematics of Richard Nowakowski (Part I)
Org: Shannon Fitzpatrick (University of Prince Edward Island)

NANCY CLARKE, Acadia University
Cops and Robbers with Gangs  [PDF]

A variation of the Cops and Robber game is considered in which the robber side consists of “gangs” of robbers that can win by attacking a cop. We present results for gangs of two robbers on graphs of small girth. This is joint work with A. Sanaei.

STEPHEN FINBOW, Saint Francis Xavier University
Eternal Domination Game on King Graphs  [PDF]

The eternal domination game is a two-player game. An infinitely fast attacker repeatedly attempts to infiltrate a network, while mobile units seek to respond to each attack. A king graph has the squares of $m\times n$ chessboard for its vertices and each edge corresponds to a legal move by a king. In this talk we discuss recent advances in the eternal domination game with a focus on determining who will win (under optimal play) on a king graph.

SHANNON FITZPATRICK, University of Prince Edward Island
The Game of k-Visibility Cops and Robber  [PDF]

The game of Cops and Robber on a graph is a pursuit-evasion game in which both the Cops and Robber know the position of each player at any given moment. We consider the $k$-visibility Cops and Robber game, a variation in which the Cops are only aware of the Robber's position when the Robber is at distance at most $k$ from at least one of the Cops. Results regarding trees, chordal graph and retracts will be presented. (This is joint work with N. Clarke, D. Cox, C. Duffy, D.Dyer, and M.E. Messinger.)

NEIL MCKAY, University of New Brunswick, Saint John
Brussels Sprouts, Lattices, and Game Trees  [PDF]

A botanical walk through the garden of combinatorial games tended by Richard Nowakowski.

MARGARET-ELLEN MESSINGER, Mount Allison University
Chip Diffusion  [PDF]

A finite number of chips are assigned to the vertices of a graph. At each time-step, every vertex simultaneously sends one chip to each neighbour with fewer chips. As with chip-firing, a natural first question is whether the long term behaviour is necessarily periodic. The talk will focus on a partial answer to this question. In particular, we show that for some graph classes, the process eventually exhibits periodic behaviour. Joint work with C. Duffy, T.F. Lidbetter, and R.J. Nowakowski.


Atlantic Association for Research in the Mathematical Sciences Centre de recherches mathmatiques The Fields Institute Pacific Institute for the Mathematical Sciences Socit mathmatique du Canada Université Ryerson Office of Naval Research Science and Technology