Abstract
For graphs G 1 and G 2 , the set multipartite Ramsey number M t ( G 1 , G 2 ) = j is the smallest integer such that every factorization of graph K j × t := F 1 F 2 satisfies the following we establish exact value of the set multipartite Ramsey number M t ( P n ,W s ) for all integers condition: either F 1 contains G 1 as a subgraph or F 2 contains G 2 as a subgraph. In this paper, t ≥ 2 where P n is a path on n vertices and W s is a wheel of order s + 1 vertices with s ≥ 3, and 3 ≥ n ≥ 4.
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