On Unicyclic Ramsey (mK2, P3)−Minimal Graphs

Ramsey minimal graph is one of growing topics in Ramsey theory. The search of Ramsey minimal graphs for a combination of graphs G and H is an interesting and difficult problem. In this paper, we study the properties of Ramsey minimal graphs for G = mK2 and H = Pn. In particular, we determine all unicyclic Ramsey minimal graphs for this combination.