Triangle-free k-chromatic graphs

A graph is k-chromatic if its chromatic number is equal to k. A k-vertex-critical graph is a k-chromatic graph for which every proper induced subgraph is (k-1)-colourable and a k-critical graph is a k-chromatic graph for which every proper subgraph is (k-1)-colourable. Finally, a maximal triangle-free graph (in short, an mtf graph, see also here) is a triangle-free graph such that the insertion of any new edge forms a triangle.

The graph lists are currently only available in 'graph6' format. The larger files are compressed with gzip. This page lists the counts of the smallest triangle-free 4- and 5-chromatic graphs. Please refer to [1] for more information on how these graphs were obtained.