The complete list of Ramsey $(2K_2,K_4)$-minimal graphs

Kristiana Wijaya (Universitas Jember Indonesia)
Edy Tri Baskoro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)
Hilda Assiyatun (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)
Djoko Suprijanto (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 3, No 2 (2015): Electronic Journal of Graph Theory and Applications

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.