The Ramsey number \(R(C_8,K_8)\). (English) Zbl 1169.05026

It was conjectured by P. Erdős, R.J. Faudree, C.C Rousseau and R.H. Schelp in [J. Graph Theory 2, 53–64 (1978; Zbl 0383.05027)] that the Ramsey number \(R(C_m, K_n) = (m - 1)(n - 1) + 1\) for \(m \geq n\) except for \((m, n) = (3, 3)\). The Conjecture has been verified for \(m \leq 7\). It is shown that \(R(C_8, K_8) = 50\), which is a start on the verification of the Conjecture for \(m = 8\).


05C55 Generalized Ramsey theory


Zbl 0383.05027
Full Text: DOI


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