On Size Multipartite Ramsey Numbers for Stars versus Cycles

Abstract

For given two graphs G1 and G2, and integer j ≥ 2, the size multipartite Ramsey numbers mj(G1, G2) is the smallest integer t such that every factorization of the graph Kj×t := F1 ⊕ F2 satisfies the following condition: either F1 contains G1 or F2 contains G2. In this paper, we determine mj(S m, Cn) for j, m, n ≥ 3 where S m is a star on m vertices and Cn is a cycle on n vertices.