Cops and robbers on P_5-free graphs

01/30/2023

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by   Maria Chudnovsky, et al.

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We prove that every connected P_5-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected P_5-free graph G with independence number at least three contains a three-vertex induced path with vertices a - b - c in order, such that every neighbour of c is also adjacent to one of a,b.