  In this article we give the generalized triangle Ramsey numbers R(K3,G) of 12
005 158 of the 12 005 168 graphs of order 10. There are 10 graphs remaining for
which we could not determine the Ramsey number. Most likely these graphs need
approaches focusing on each individual graph in order to determine their
triangle Ramsey number. The results were obtained by combining new
computational and theoretical results. We also describe an optimized algorithm
for the generation of all maximal triangle-free graphs and triangle Ramsey
graphs. All Ramsey numbers up to 30 were computed by our implementation of this
algorithm. We also prove some theoretical results that are applied to determine
several triangle Ramsey numbers larger than 30. As not only the number of
graphs is increasing very fast, but also the difficulty to determine Ramsey
numbers, we consider it very likely that the table of all triangle Ramsey
numbers for graphs of order 10 is the last complete table that can possibly be
determined for a very long time.
