\(R(C_n,C_n,C_n)\leqq (4+o(1))n\)
type: Item
instance of: scholarly article
title: \(R(C_n,C_n,C_n)\leqq (4+o(1))n\)
zbMATH Open document ID: 0934.05091
author: Tomasz Łuczak
published in: Journal of Combinatorial Theory. Series B
publication date: 1999-11-29T00:00:00Z
review text: Any coloring of ``almost all'' the edges of \(K_{4(1 + \eta)n}\) with three colors yields a monochromatic odd cycle of length at least \((1 + {\eta /10})n\), for every \(0 < \eta <10^{-5}\) and \(n \geq \exp(\eta ^{-50})\). It follows that the Ramsey number \(R(C_n,C_n,C_n)\) is bounded from above by \((4+o(1))n\). If \(n\) is odd, \(R(C_n,C_n,C_n)=(4+o(1))n\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1346892
zbMATH Keywords: Ramsey number
reviewed by: Norman F. Quimpo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1346892