D. Rahmadani, H. Assiyatun, E.T. Baskoro
If G, H and F are finite and simple graphs, notation F → (G, H) means that for any red-blue coloring of the edges of F, there is either a red subgraph isomorphic to G or a blue subgraph isomorphic to H. A graph F is a Ramsey (G, H)-minimal graph if F → (G, H) and for every e ∈ E(F), graph F-e n (G, H). The class of all Ramsey (G, H)-minimal graphs (up to isomorphism) will be denoted by R(G, H). The characterization of all graphs in the infinite class R(P3, Pn ) is still open, for any n ≥ 4. In this paper, we find an infinite families of trees in R(P3, P5). We determine how to construct unicyclic graphs in R(P3, Pn ), for any n ≥ 5 from trees in the same class. Further, we give some properties for the unicyclic graphs constructed from trees in R(P3, Pn ), for any n ≥ 5. © Published under licence by IOP Publishing Ltd.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Indonesia; Combinatorial Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Indonesia
