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Title: The Ramsey numbers for a cycle of length six or seven versus a clique of order seven
Authors: Cheng, T. C. Edwin
Chen, Yaojun
Zhang, Yunqing
Ng, Chi-to Daniel
Subjects: Ramsey number
Complete graph
Issue Date: 6-May-2007
Publisher: Elsevier
Source: Discrete mathematics, May 2007, v. 307, no. 9-10, p.1047-1053.
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. It was conjectured that R(C[sub m],K[sub n])=(m-1)(n-1)+1 for m≥n≥3 and (m,n)≠(3,3). We show that R(C[sub 6],K[sub 7])=31 and R(C[sub 7],K[sub 7])=37, and the latter result confirms the conjecture in the case when m=n=7.
Rights: Discrete Mathematics © 2006 Elsevier. The journal web site is located at
Type: Journal/Magazine Article
DOI: 10.1016/j.disc.2006.07.036
ISSN: 0012-365X
Appears in Collections:LMS Journal/Magazine Articles

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