Bounding Ramsey numbers through large deviation inequalities

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Abstract

We develop a new approach for proving lower bounds for various Ramsey numbers, based on using large deviation inequalities. This approach enables us to obtain the bounds for the off‐diagonal Ramsey numbers R(Kr, Kk), r ≤ k, that match the best known bounds, obtained through the local lemma. We discuss also the bounds for a related Ramsey‐type problem and show, for example, that there exists a K4‐free graph G on n vertices in which every cn3/5 log1/2 n vertices span a copy of K3. © 1995 John Wiley & Sons, Inc.

Original languageEnglish
Pages (from-to)145-155
Number of pages11
JournalRandom Structures and Algorithms
Volume7
Issue number2
DOIs
StatePublished - Sep 1995

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