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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Assiyatun, Hilda
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, ITB
Electrical & Electronics Engineering

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On Ramsey (2K2, Wn)-minimal graphs of smallest order Fajri, Muhammad Rafif; Assiyatun, Hilda; Baskoro, Edy Tri
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.7

Abstract

The notation F → (H, G) 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 H or the subgraph of F induced by all blue edges contains a graph G. Let R(H, G) denote the set of all graphs F satisfying F → (H, G) and for every e ∈ E(F), (F − e) ↛ (H, G). In this paper, we propose some properties of Ramsey (2K2, G)-minimal graph of smallest order, where G is a graph containing a dominating vertex. We also find all members of R(2K2, Wn) of smallest order for n ∈ [5,8].
Co-Authors Baskoro, Edy Tri Fajri, Muhammad Rafif