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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 givearXiv:1812.09955v1 fatcat:zstyl44sofbjtotmkzgwpumqwi