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arXiv · 1901.01658

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

Chula Jayawardene·Lilanthi Samarasekara
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Abstract

A graph on 5 vertices consisting of 2 copies of the cycle graph C3 sharing a common vertex is called the Butterfly graph (B). The smallest natural number s such that any two-colouring (say red and blue) of the edges of Kj*s has a copy of a red B or a blue G is called the multipartite Ramsey number of Butterfly graph versus G. This number is denoted by mj(B,G). In this paper we find exact the values for mj(B,G) when and G represents any connected proper subgraph of K4 with at least one edge.

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Chula Jayawardene, Lilanthi Samarasekara. 2019-01-07. A Ramsey problem related to butterfly graph vs. proper connected subgraphs of K4. https://arxiv.org/abs/1901.01658

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