On Ramsey minimal graphs (Q5917560)

Let \(G,F\) and \(H\) be graphs. Then \(G\) is \(\left( F,H\right) \)-Ramsey minimal if any colouring of the edges of \(G\) in red and blue yields a red copy of \(F\) or a blue copy of \(H\), but no proper subgraph of \(G\) has this property. This paper gives two equivalent theorems which characterize the \(\left( K_{1,2},K_{1,m}\right) \) Ramsey minimal graphs.