Asymptotic bounds for irredundant and mixed Ramsey numbers

The irredundant Ramsey number s(m, n) is the smallest N such that in every red‐blue coloring of the edges of K N , either the blue graph contains an m ‐element irredundant set or the red graph contains an n ‐element irredundant set. The definition of the mixed Ramsey number t(m, n) differs from s(m, n) in that the n ‐element irredundant set is replaced by an n ‐element independent set. We prove asymptotic lower bounds for s(n, n) and t(m, n) (with m fixed and n large) and a general upper bound for t (3, n ). © 1993 John Wiley & Sons, Inc.