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Title: The Ramsey numbers R(C[sub m], K[sub 7]) and R(C[sub 7], K[sub 8])
Authors: Chen, Yaojun
Cheng, T. C. Edwin
Zhang, Yunqing
Subjects: Ramsey number
Complete graph
Issue Date: Jul-2008
Publisher: Elsevier Ltd.
Source: European journal of combinatorics, July 2008, v. 29, no. 5, p. 1337-1352.
Abstract: For two given graphs G₁ and G₂, the Ramsey number R(G₁, G₂) is the smallest integer n such that for any graph G of order n, either G contains G₁ or the complement of G contains G₂. Let C[sub m] denote a cycle of length m and K[sub n] a complete graph of order n. In this paper we show that R(C[sub m], K[sub 7]) = 6m − 5 for m ≥ 7 and R(C[sub 7], K[sub 8]) = 43, with the former result confirming a conjecture due to Erdös, Faudree, Rousseau and Schelp that R(C[sub m], K[sub n]) = (m − 1)(n − 1)+ 1 for m ≥ n ≥ 3 and (m,n) ≠ (3,3) in the case where n = 7.
Rights: European Journal of Combinatorics © 2007 Elsevier Ltd. The journal web site is located at
Type: Journal/Magazine Article
DOI: 10.1016/j.ejc.2007.05.007
ISSN: 0195-6698
Appears in Collections:LMS Journal/Magazine Articles

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