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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Hilda Assiyatun
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia
Electrical & Electronics Engineering

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The complete list of Ramsey $(2K_2,K_4)$-minimal graphs Kristiana Wijaya; Edy Tri Baskoro; Hilda Assiyatun; Djoko Suprijanto
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (2015): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2015.3.2.9

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.
Co-Authors Djoko Suprijanto Edy Tri Baskoro Kristiana Wijaya