On Ramsey (2K2, Wn)-minimal graphs of smallest order - Fajri, Muhammad Rafif; Assiyatun, Hilda; Baskoro, Edy Tri (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
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].