The Ramsey numbers \(R(C_m,K_7)\) and \(R(C_7,K_8)\)
type: Item
instance of: scholarly article
title: The Ramsey numbers \(R(C_m,K_7)\) and \(R(C_7,K_8)\)
zbMATH Open document ID: 1154.05044
author: Yaojun Chen
author: Yunqing Zhang
author: T. C. Edwin Cheng
published in: European Journal of Combinatorics
publication date: 2008-05-29T00:00:00Z
review text: The Ramsey number \(R(G_1,G_2)\) is the smallest integer \(n\) such that for any \(G\) of order \(n\) either \(G\) contains \(G_1\) or the complement of \(G\) contains \(G_2\). In the paper it is shown that \(R(C_m,K_7) = 6m-5\) for \(m \geq 7\) and \(R(C_7,K_8) = 43\). These results confirm the conjecture of \textit{P. Erdős}, \textit{R.J. Faudree}, \textit{C.C. Rousseau}, and \textit{R.H. Schelp} [J. Graph Theory 2, 53--64 (1978; Zbl 0383.05027)].
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 5280772
zbMATH Keywords: Ramsey number
zbMATH Keywords: cycle
zbMATH Keywords: complete graph
reviewed by: Gabriel Semanišin
MaRDI profile type: Publication
full work available at URL: j.ejc.2007.05.007
OpenAlex ID: W1504442794
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DOI: 10.1016/J.EJC.2007.05.007
description: scientific article; zbMATH DE number 5280772