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Pure pairs. II. Excluding all subdivisions of a graph

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Date

2021-06-01

Authors

Chudnovsky, Maria
Scott, Alex
Seymour, Paul
Spirkl, Sophie

Advisor

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Publisher

Springer Nature

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.

Description

This is a post-peer-review, pre-copyedit version of an article published in Combinatorica. The final authenticated version is available online at: https://doi.org/10.1007/s00493-020-4024-1

Keywords

pure pairs, Erdos-Hanjnal conjecture

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