G.A. Muttaqin, D. Rahmadani, Purwanto, I.M. Sulandra
Let F, G and H be graphs. Notation F → (G, H) means that there is any two-coloring, say red and blue, of all edges of F which contains red subgraph isomorphic to G or blue subgraph isomorphic to H. The graph F is Ramsey (G, H)-minimal if F → (G, H) but F-e n (G, H) for any e ∈ E(F).The class of all Ramsey (G, H)-minimal graphs will be denoted by R(G, H). According to the previous study, we know that graphs in R(P 3, C 7) have at least 13 edges.In this paper, we find graphs in R(P 3, C 7) having seven vertices and 13 and 14 edges, respectively. Further, we give some necessary conditions for Ramsey (P 3, C 7)-minimal graphs with seven vertices. © Published under licence by IOP Publishing Ltd.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Indonesia
