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A graph on 5 vertices consisting of 2 copies of the cycle graph C3 sharing acommon vertex is called the Butterfly graph (B). The smallest natural number ssuch that any two-colouring (say red and blue) of the edges of Kj*s has a copyof a red B or a blue G is called the multipartite Ramsey number of Butterflygraph versus G. This number is denoted by mj(B,G). In this paper we find exactthe values for mj(B,G) when and G represents any connected proper subgraph ofK4 with at least one edge.

A Ramsey problem related to butterfly graph vs. proper connected subgraphs of K4