The generation of maximal triangle-free graphs (Q1576571)

The authors describe an algorithm to enumerate all maximal triangle-free graphs of a given vertex-number. The number of such graphs grows of course exponentially, but it begins quite small. So the authors were able to implement that algorithm and to obtain all maximal triangle-free graphs for up to 21 vertices. For these they tested several conjectures on triangle-free graphs, and obtained some new triangle Ramsey numbers (triangle versus a set of graphs).