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).