The game of sandwich cops and robber
LE3 .A278 2018
Bachelor of Science
Mathematics and Statistics
Mathematics & Statistics
The game of Cops and Robber is a vertex-to-vertex pursuit game played on an undirected graph. The game of Sandwich Cops and Robber is a variation of this game in which the robber is located on the edges of the graph. In order to capture the robber, the cops must move so that at least one cop occupies each endpoint of the edge on which the robber is located. We compare this new game to the original game of Cops and Robber, examining the relationship between the copnumber and the sandwich copnumber of particular classes of graphs, including graph products. We identify certain properties of graphs that cause the sandwich copnumber to differ from the copnumber. Additionally, we introduce a variation of Sandwich Cops and Robber in which the cops move from vertex to vertex along the non-edges of a graph, rather than the edges. We find the disjoint sandwich copnumber of several classes of graphs, as well as providing bounds on the disjoint sandwich copnumber of a graph in terms of its domination number.
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