The Ramsey number for a cycle of length six versus a clique of order eight

Authors:
Yaojun Chen;T. C. Edwin Cheng;Ran Xu
Affiliations:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China;Department of Logistics, The Hong Kong Polytechnic University, Hung Kom, Kowloon, Hong Kong, China;Department of Mathematics, Nanjing University, Nanjing 210093, PR China
Venue:
Discrete Applied Mathematics
Year:
2009

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The Ramsey numbers R(Cm,K7) and R(C7,K8)

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All cycle-complete graph Ramsey numbers r(Cm, K6)

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The Ramsey number for a cycle of length six versus a clique of order eight

Discrete Applied Mathematics

The Ramsey number for a cycle of length six versus a clique of order eight

Discrete Applied Mathematics

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Abstract

For two given graphs G"1 and G"2, the Ramsey number R(G"1,G"2) is the smallest integer n such that for any graph G of order n, either G contains G"1 or the complement of G contains G"2. Let C"m denote a cycle of length m and K"n a complete graph of order n. In this paper, it is shown that R(C"6,K"8)=36.