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

Small minimal $(3, 3)$-Ramsey graphs