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arXiv · 1408.1964

The Erd\H{o}s-Hajnal Conjecture for Long Holes and Anti-holes

Marthe Bonamy·Nicolas Bousquet·Stéphan Thomassé
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Abstract

Erd\H{o}s and Hajnal conjectured that, for every graph $H$, there exists a constant $c_H$ such that every graph $G$ on $n$ vertices which does not contain any induced copy of $H$ has a clique or a stable set of size $n^{c_H}$. We prove that for every $k$, there exists $c_k>0$ such that every graph $G$ on $n$ vertices not inducing a cycle of length at least $k$ nor its complement contains a clique or a stable set of size $n^{c_k}$.

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Marthe Bonamy, Nicolas Bousquet, Stéphan Thomassé. 2014-08-08. The Erd\H{o}s-Hajnal Conjecture for Long Holes and Anti-holes. https://arxiv.org/abs/1408.1964

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