Cops, robbers, and burning bridges [article]

William B. Kinnersley, Eric Peterson
2018 arXiv   pre-print
We consider a variant of Cops and Robbers wherein each edge traversed by the robber is deleted from the graph. The focus is on determining the minimum number of cops needed to capture a robber on a graph G, called the bridge-burning cop number of G and denoted c_b(G). We determine c_b(G) exactly for several elementary classes of graphs and give a polynomial-time algorithm to compute c_b(T) when T is a tree. We also study two-dimensional square grids and tori, as well as hypercubes, and we give
more » ... ounds on the capture time of a graph (the minimum number of rounds needed for a single cop to capture a robber on G, provided that c_b(G) = 1).
arXiv:1812.09955v1 fatcat:zstyl44sofbjtotmkzgwpumqwi