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The Ramsey numbers \(R(C_m,K_7)\) and \(R(C_7,K_8)\). (English) Zbl 1154.05044

The Ramsey number \(R(G_1,G_2)\) is the smallest integer \(n\) such that for any \(G\) of order \(n\) either \(G\) contains \(G_1\) or the complement of \(G\) contains \(G_2\). In the paper it is shown that \(R(C_m,K_7) = 6m-5\) for \(m \geq 7\) and \(R(C_7,K_8) = 43\). These results confirm 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)].

MSC:

05C55 Generalized Ramsey theory

Citations:

Zbl 0383.05027
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References:

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