The irredundant ramsey number s(3,3,3) = 13

Let G 1 , G 2 ,. …, G t be an arbitrary t ‐edge coloring of K n , where for each i ∈ {1,2, …, t }, G i is the spanning subgraph of K n consisting of all edges colored with the i th color. The irredundant Ramsey number s ( q 1 , q 2 , …, q t ) is defined as the smallest integer n such that for any t ‐edge coloring of K n , i has an irredundant set of size q i for at least one i ∈ {1,2, …, t }. It is proved that s(3,3,3) = 13, a result that improves the known bounds 12 ≤ s(3,3,3) ≤ 14.