Pure pairs. II. Excluding all subdivisions of a graph
Abstract
We prove for every graph H there exists ɛ > 0 such that, for every graph G with |G|≥2, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least ɛ|G| neighbours, or there are two disjoint sets A, B ⊆ V(G) with |A|,|B|≥ɛ|G| such that no edge joins A and B. It follows that for every graph H, there exists c>0 such that for every graph G, if no induced subgraph of G or its complement is a subdivision of H, then G has a clique or stable set of cardinality at least |G|c. This is related to the Erdős-Hajnal conjecture.
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Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl
(2021).
Pure pairs. II. Excluding all subdivisions of a graph. UWSpace.
http://hdl.handle.net/10012/18505
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