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

Authors:
Yaojun Chen;T. C. Edwin Cheng;Yunqing Zhang
Affiliations:
Department of Mathematics, Nanjing University, Nanjing 210093, China;Department of Logistics, The Hong Kong Polytechnic University, Hung Kom, Kowloon, Hong Kong, China;Department of Mathematics, Nanjing University, Nanjing 210093, China
Venue:
European Journal of Combinatorics
Year:
2008

Citing 2
Cited 1

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Graph Theory With Applications
All cycle-complete graph Ramsey numbers r(Cm, K6)

Journal of Graph Theory

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 we show that R(C"m,K"7)=6m-5 for m=7 and R(C"7,K"8)=43, with the former result confirming a conjecture due to Erdos, Faudree, Rousseau and Schelp that R(C"m,K"n)=(m-1)(n-1)+1 for m=n=3 and (m,n)(3,3) in the case where n=7.