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Almost All F-Free Graphs Have The Erdos-Hajnal Property

Abstract : Erdős and Hajnal conjectured that, for every graph H, there exists a constant ɛ(H) > 0 such that every H-free graph G (that is, not containing H as an induced subgraph) must contain a clique or an independent set of size at least |G|ɛ( H). We prove that there exists ɛ(H) such that almost every H-ïvee graph G has this property, meaning that, amongst the if-free graphs with n vertices, the proportion having the property tends to one as n → ∞.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00806800
Contributor : Alexandre Pinlou <>
Submitted on : Tuesday, April 2, 2013 - 1:35:02 PM
Last modification on : Friday, September 18, 2020 - 6:06:02 PM

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Martin Loebl, Bruce Reed, Alex Scott, Andrew Thomason, Stéphan Thomassé. Almost All F-Free Graphs Have The Erdos-Hajnal Property. An Irregular Mind, 21, pp.405-414, 2010, ⟨10.1007/978-3-642-14444-8_11⟩. ⟨lirmm-00806800⟩

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