On Ramsey (2K2, Wn)-minimal graphs of smallest order

Fajri, Muhammad Rafif (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, ITB)
Assiyatun, Hilda (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, ITB)
Baskoro, Edy Tri (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, ITB)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications

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].