On size multipartite Ramsey numbers of large paths versus wheel on five vertices.

For given two graphs G 1 and G 2 , and integer j ≥ 2 , the size multipartite Ramsey number m j (G 1 , G 2) = t is the smallest integer such that every factorization of graph K j × t : = F 1 ⊕ F 2 satisfies the following condition: either F 1 contains G 1 as a subgraph or F 2 contains G 2 as a subgraph. In this paper, we determine that m 4 (P n , W 4) for n ≥ 2 where P n is path on n ≥ 2 vertices and W 4 is a wheel on five vertices. [ABSTRACT FROM AUTHOR]