The Ramsey number
Summary: For two given graphs \(G_1\) and \(G_2\), the Ramsey number \(r(G_1, G_2)\) is the smallest integer \(n\) such that for any graph \(G\) of order \(n\), either \(G\) contains \(G_1\) or the complement of \(G\) contains \(G_2\). Let \(K_m\) denote a complete graph of order \(m\) and \(K_n - P_3\) a complete graph of order \(n\) without two incident edges. In this paper, we prove that \(r(K_5 - P_3, K_5) = 25\) without help of computer algorithms.
scientific article; zbMATH DE number 5903020