THE IRREDUNDANT RAMSEY NUMBER S(3,3,3)=13

Let G1, G2,..., G(t) be an arbitrary t-edge coloring of K(n), where fo r each i is-an-element-of {1, 2,..., t}, G(i) is the spanning subgraph of K(n) consisting of all edges colored with the ith color. The irred undant Ramsey number s(q1, q2,..., q(t)) is defined as the smallest in teger n such that for any t-edge coloring of K(n), G(i)BAR has an irre dundant set of size q(i) for at least one i is-an-element-of {1, 2, .. ., t}. It is proved that s(3, 3, 3) = 13, a result that improves the known bounds 12 less-than-or-equal-to s(3,3,3) less-than-or-equal-to 1 4. (C) 1994 John Wiley & Sons, Inc.