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 on the independence number and new lower bounds on the minimum degree of arbitrary $(3,3)$-Ramsey graphs.