Abstract

A fan F_n is defined as the graph P_n+K_1 where P_n  is the path on n vertices. The notation F \arrowing (G,H) means that if all edges of f are arbitrarily colored by red or blue, then either the subgraph of  induced by all red edges contains a graph G or the subgraph of F induced by all blue edges contains a graph H. Let \mathcal{R}(G,H) denote the set of all graphs F satisfying F \arrowing (G,H) and for every e \in E(F).  In this paper, we propose characterization for a graph F of minimum order that belongs to  \mathcal{R}(2K_2,F_n) with minimum order, for n \in [3,6].

Fan, Matching, Ramsey minimal graph.