2018/04/09 by Lu, Linyuan, Wang, Zhiyu
#05C57 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1804.02802
In the cops and robber games played on a simple graph G, Aigner and Fromme's lemma states that one cop can guard a shortest path in the sense that the robber cannot enter this path without getting caught after finitely many steps. In this paper, we extend Aigner and Fromme's lemma to cover a larger family of graphs and give metric characterizations of these graphs. In particular, we show that a generalization of block graphs, namely vertebrate graphs, are 1-guardable. We use this result to give the cop number of some special class of multi-layer generalized Peterson graphs.