  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.
