The Ramsey numbers for a cycle of length six or seven versus a clique of order seven
The authors considers Ramsey numbers for cycles of length 6 or 7. 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 \(G_2\). The authors mainly show that \(R(C_6,K_7)=31\) where \(C_m\) denotes a cycle of length \(m\) and \(K_n\) a complete graph of order \(n\).
scientific article; zbMATH DE number 5134173