On Ramsey (K _1,2 ,C ₄ )-minimal graphs

Abstract

For graphs F , G and H, we write F ! (G; H) to mean that any red-blue coloring of the edges of F contains a red copy of G or a blue copy of H. The graph F is Ramsey (G; H)-minimal if F ! (G; H) but F 9 (G; H) for any proper subgraph F F . We present an innite family of Ramsey (K1;2; C4)-minimal graphs of any diameter 4.