PIMS-UVic Discrete Math Seminar: Nancy Clarke

Cops and Robber is a well-studied pursuit-evasion game played on graphs. In this talk, I’ll discuss a variation of the game with a new capture condition. Instead of a win for the cop side resulting from at least one of the cops occupying the same vertex as the robber as in the original game, the cops in this surrounding version win by occupying each of the robber's neighbouring vertices. The surrounding copnumber is analogous to the copnumber. We present a variety of results for this parameter, including exact values for several classes of graphs as well as more general bounds. Classes of interest include graph products, graphs arising from combinatorial designs, and generalized Petersen graphs. This is joint work with A. Burgess, R. Cameron, P. Danziger, S. Finbow, C. Jones, and D. Pike.