New upper bounds for Ramsey numbers

Ramsey number R(G(1),G(2)) is the smallest integer p such that for any graph G on p vertices either G contains G(1) or (G) over bar contains G(2), where (G) over bar denotes the complement of G. Let R(m, n) = R(K-m, K-n). Some new upper bound formulas are obtained for R(G(1),G(2)) and R(m, n), and we derive some new upper bounds for Ramsey numbers here. (C) 1998 Academic Press Limited.