Let G_1, G_2, ..., G_t be a t-graph edge coloring of the complete graph K_n, where for each i = 1, 2, ..., t, G_i is the spanning subgraph of K_n consisting of all graph edges colored with the ith color. The irredundant Ramsey number s(q_1, ..., q_t) is the smallest integer n such that for any t-graph edge coloring of K_n, the graph complement (G_i)^_ has an irredundant set of size q_i for at least one i = 1, ..., t. Irredundant Ramsey numbers were introduced by Brewster et al. (1989) and satisfy s(q_1, ..., q_t)<=R(q_1, ..., q_t). For a summary, see Mynhardt.