SMALL MINIMAL (3, 3)-RAMSEY GRAPHS

We say that $G$ is a (3, 3)-Ramsey graph if every 2-coloring of the edges of $G$ forces a monochromatic triangle. The (3, 3)-Ramsey graph $G$ is minimal if $G$ does not contain a proper (3, 3)-Ramsey subgraph. In this work we find all minimal (3, 3)-Ramsey graphs with up to 13 vertices with the help of a computer, and we obtain some new results for these graphs. We also obtain new upper bounds for the independence number and new lower bounds for the minimum degree of arbitrary (3, 3)-Ramsey graphs.