On graphs for which large books are Ramsey good

Abstract Let be a graph and a connected graph. Then is said to be ‐good if the Ramsey number is equal to the general lower bound , where and are the chromatic number and the chromatic surplus of , respectively. For a fixed graph with and , it is shown that if , then large are ‐good if and only if is a subgraph of for some , where is a matching of edges. We also give conditions for with respect to ‐goodness of large .