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W2471806395 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." @default.
W2471806395 created "2016-07-22" @default.
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W2471806395 date "2015-08-04" @default.
W2471806395 modified "2023-09-23" @default.
W2471806395 title "Excluding hooks and their complements" @default.
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