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On a conjecture involving cycle-complete graph Ramsey numbers. (English) Zbl 0963.05094

A well-known result of J. A. Bondy and P. Erdős [J. Comb. Theory, Ser. B 14, 46-54 (1973; Zbl 0248.05127)] for cycle-complete graph Ramsey numbers is that \(r(C_n,K_m) = (m-1)(n-1)+1\) for all \(n \geq m^2 -2\). The authors prove the conjecture that this equation holds for all \((n,m) \neq (3,3)\) with \(n \geq m\) for the case \(m=5\).

MSC:

05C55 Generalized Ramsey theory

Citations:

Zbl 0248.05127
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