The Ramsey numbers \(R(C_m,K_7)\) and \(R(C_7,K_8)\)
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 \textit{P. Erdős}, \textit{R.J. Faudree}, \textit{C.C. Rousseau}, and \textit{R.H. Schelp} [J. Graph Theory 2, 53--64 (1978; Zbl 0383.05027)].
scientific article; zbMATH DE number 5280772