Minimum Degrees of Minimal Ramsey Graphs for Almost-Cliques

For graphs F and H, we say F is Ramsey for H if every 2-coloring of the edges of F contains a monochromatic copy of H. The graph F is Ramsey H-minimal if F is Ramsey for H and there is no proper subgraph F' of F so that F' is Ramsey for H. Burr etï¾źal. defined sH to be the minimum degree of F over all Ramsey H-minimal graphs F. Define Ht,d to be a graph on t+1 vertices consisting of a complete graph on t vertices and one additional vertex of degree d. We show that sHt,d=d2 for all values 1更多