Excluding hooks and their complements
نویسندگان
چکیده
The celebrated Erdős-Hajnal conjecture states that for every n-vertex undirected graph H there exists ε(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. 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. 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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تاریخ انتشار 2017