The Ramsey numbers for a cycle of length six or seven versus a clique of order seven

: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Cm denote a cycle of length m and Kn a complete graph of order n. It was conjectured that R(Cm, Kn) = (m−1)(n−1)+1 for m ≥ n ≥ 3 and (m, n) = (3, 3). We show that R(C6, K7) = 31 and R(C7, K7) = 37, and the latter result confirms the conjecture in the case when m = n = 7. Key words: Ramsey number, Cycle, Complete graph

• Type: Journal
• Year: 2007
• Where: DM
• Authors: T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. T. Ng
• Keywords: Complete Graph, DM 2007, Ramsey Number, Smallest Integer