On Ramsey minimal graphs Original Research Article

For graphs G, F and H we write G→(F,H) to mean that if the edges of G are coloured with two colours, say red and blue, then the red subgraph contains a copy of F or the blue subgraph contains a copy of H. The graph G is (F,H)-minimal (Ramsey-minimal) if G→(F,H) but G′↛(F,H) for any proper subgraph G′⊆G. The class of all (F,H)-minimal graphs will be denoted by R(F,H). In this paper we will give two equivalent theorems which characterize the graphs belonging to R(K1,2,K1,m) for m⩾3.