On Ramsey (K_{1,2},K_{n})-minimal graphs

Let F be a graph and let G, H denote nonempty families of graphs. We write F → (G,H) if in any 2-coloring of edges of F with red and blue, there is a red subgraph isomorphic to some graph from G or a blue subgraph isomorphic to some graph from H. The graph F without isolated vertices is said to be a (G,H)-minimal graph if F → (G,H) and F − e 6→ (G,H) for every e ∈ E(F ). We present a technique which allows to generate infinite family of (G,H)minimal graphs if we know some special graphs. In particular, we show how to receive infinite family of (K1,2,Kn)-minimal graphs, for every n ≥ 3.