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The cycle-complete graph Ramsey number \(r(C_8,K_8)\). (English) Zbl 1144.05042

It is shown that the Ramsey number \(R(C_8, K_8) = 50\). This is consistent with and confirms the conjecture of P. Erdős, R. J. Faudree, C.C. Rousseau, and R. H. Schelp [J. Graph Theory 2, 53–64 (1978; Zbl 0383.05027)] that \(R(C_m, K_n) = (m - 1)(n - 1) + 1\) for \(n \geq m \geq 3\) if \((m, n) \neq (3,3)\) in the case when \(m = n = 8\).

MSC:

05C55 Generalized Ramsey theory
05C35 Extremal problems in graph theory

Citations:

Zbl 0383.05027
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