R(5,5) > 42

The two coloring of the edges of K42 which established the lower bound is available as a 0-1 adjacency matrix .

This bound was established in 1987 (by me, not by McKay and Radziszowski, as is often claimed). A fairly complex genetic algorithm was used. Since then I've found very simple methods that can produce the same construction, with the aid of much faster computers.

Geoff Exoo