On multicolor Ramsey numbers for even cycles in graphs

The multicolor Ramsey number R-r(H) is defined to be the smallest integer n = n(r) with the property that any r-coloring of the edges of complete graph K-n must result in a monochromatic subgraph of K-n isomorphic to H. In this paper, we study the case that H is a cycle of length 2k. If 2k >= r + 1 and r is a prime power, we show that R-r(C-2k) > r(2) + 2k - r - 1.