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We prove that every connected P5-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected P5-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 neighbor of c is also adjacent to one of a,b.more » « less
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Eppstein, David; Hickingbotham, Robert; Merker, Laura; Norin, Sergey; Seweryn, Michał T; Wood, David R (, Discrete & Computational Geometry)
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Balogh, József; Clemen, Felix Christian; Lidický, Bernard; Norin, Sergey; Volec, Jan (, SIAM Journal on Discrete Mathematics)
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Balogh, József; Lidický, Bernard; Norin, Sergey; Pfender, Florian; Salazar, Gelasio; Spiro, Sam (, Procedia Computer Science)
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Blumenthal, Adam; Lidický, Bernard; Martin, Ryan R.; Norin, Sergey; Pfender, Florian; Volec, Jan (, SIAM Journal on Discrete Mathematics)
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Král’, Daniel; Noel, Jonathan A; Norin, Sergey; Volec, Jan; Wei, Fan (, Combinatorica)
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