A note on Ramsey numbers with two parameters

1 The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices2 either G contains G1 or G contains G2, where G denotes the complement of G. In this paper, some3 new bounds with two parameters for the Ramsey number R(G1, G2), under some assumptions, are4 obtained. Especially, we prove that R(K6 - e, K6) 116 and R(K6 - e, K7) 202, these improve5 the two upper bounds for the classical Ramsey number in [S.P. Radziszowski, Small Ramsey number,6 Electron. J. Combin. DS1 (2002) 1

• Type: Journal
• Year: 2006
• Where: EJC
• Authors: Yi Ru Huang, Jian Sheng Yang, Kemin Zhang
• Keywords: Classical Ramsey Number, EJC 2006, EJC 2007, Ramsey Number, Smallest Integer