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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© 2010 János Bolyai Mathematical Society and Springer-Verlag
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Loebl, M., Reed, B., Scott, A., Thomason, A., Thomassé, S. (2010). Almost All F-Free Graphs Have The Erdös-Hajnal Property. In: Bárány, I., Solymosi, J., Sági, G. (eds) An Irregular Mind. Bolyai Society Mathematical Studies, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14444-8_11
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DOI: https://doi.org/10.1007/978-3-642-14444-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14443-1
Online ISBN: 978-3-642-14444-8
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