On the minimum degree of minimal Ramsey graphs

We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr et al. We determine the corresponding graph parameter for numerous bipartite graphs, including bi-regular bipartite graphs and forests. We also make initial progress for graphs of larger chromatic number. Numerous interesting problems remain open. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 150–164, 2010