Cops and robbers on $P_5$-free graphs

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 \hbox{-} b \hbox{-}...

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Bibliographic Details
Main Authors Chudnovsky, Maria, Norin, Sergey, Seymour, Paul, Turcotte, Jérémie
Format Journal Article
LanguageEnglish
Published 30.01.2023
Subjects
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Summary: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 $a \hbox{-} b \hbox{-} c$ in order, such that every neighbour of $c$ is also adjacent to one of $a,b$.
DOI:10.48550/arxiv.2301.13175