On graphsG for which all large trees areG-good

LetG be a graph satisfying x(G) = k. The following problem is considered: WhichG have the property that, if n is large enough, the Ramsey numberr(G, T) has the value (k -- 1)(n -- 1) + 1 for all treesT onn vertices? It is shown thatG has this property if and only if for somem, G is a subgraph of bothL k,m andM K.m , whereL k,m andM k,m are two particulark-chromatic graphs. Indeed, it is shown thatr(L k,m ,M k,m ,T n ) = (k -- 1)(n -- 1) + 1 whenn is large.