On the three color Ramsey numbers R(Cm, C4, C4)

Let G(i) be the subgraph of G whose edges are in the i-th color in an r-coloring of the edges of G. If there exists an r-coloring of the edges of G such that H-i not subset of G(i) for all 1 <= i <= r, then G is said to be r-colorable to (H-1, H-2,..., H-r). The multicolor Ramsey number R(H-1, H-2, ..., H-r) is the smallest integer n such that K-n is not r-colorable to (H-1, H-2,..., H-r). It is well known that R(C-m, C-4, C-4) m + 2 for sufficiently large m. In this paper, we determine the values of R(C-m, C-4, C-4) for m >= 5, which show that R(C-m, C-4, C-4) = m + 2 for m >= 11.