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description Journal article public Electronic Journal of Graph Theory and Applications

The Complete List of Ramsey $(2K_2,K_4)$-minimal Graphs

Kristiana Wijaya, Edy Tri Baskoro, Hilda Assiyatun, Djoko Suprijanto
Published 2015

Abstract

Let $F, G,$ and $H$ be non-empty graphs. The notation $F \rightarrow (G,H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F$ induced by all blue edges contains a graph $H.$ A graph $F$ satisfying two conditions: $F \rightarrow (G,H)$ and $(F-e) \nrightarrow (G,H)$ for every $e \in E(F)$ is called a Ramsey $(G,H)-$minimal graph. In this paper, we determine all non-isomorphic Ramsey $(2K_2,K_4)$-minimal graphs.

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