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arXiv · 1508.00634

Excluding hooks and their complements

Krzysztof Choromanski·Dvir Falik·Anita Liebenau·Viresh Patel·Marcin Pilipczuk
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Abstract

The celebrated Erdos-Hajnal conjecture states that for every $n$-vertex undirected graph $H$ there exists $\eps(H)>0$ such that every graph $G$ that does not contain $H$ as an induced subgraph contains a clique or an independent set of size at least $n^{\eps(H)}$. A weaker version of the conjecture states that the polynomial-size clique/independent set phenomenon occurs if one excludes both $H$ and its complement $H^{\compl}$. We show that the weaker conjecture holds if $H$ is any path with a pendant edge at its third vertex; thus we give a new infinite family of graphs for which the conjecture holds.

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Krzysztof Choromanski, Dvir Falik, Anita Liebenau, Viresh Patel, Marcin Pilipczuk. 2015-08-04. Excluding hooks and their complements. https://arxiv.org/abs/1508.00634

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