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

Abstract

For given two graphs [Formula: see text] and [Formula: see text], and integer [Formula: see text], the size multipartite Ramsey number [Formula: see text] is the smallest integer such that every factorization of graph [Formula: see text] satisfies the following condition: either [Formula: see text] contains [Formula: see text] as a subgraph or [Formula: see text] contains [Formula: see text] as a subgraph. In this paper, we determine that [Formula: see text] for [Formula: see text] where [Formula: see text] is path on [Formula: see text] vertices and [Formula: see text] is a wheel on five vertices.