R(3,4,5) > 79

R(3,3,3,4) > 86

Both colorings are circle colorings. The colors assigned to each chord length are listed below. The 2nd color in the R(3,3,3,4) construction is interesting.


R(3,4,5) > 79:

Color 1:  5,  8, 11, 14, 17, 21, 23, 24, 27, 30, 36
Color 2:  3,  4,  7,  9, 15, 16, 18, 19, 26, 32, 37, 38, 39
Color 3:  1,  2,  6, 10, 12, 13, 20, 22, 25, 28, 29, 31, 33, 34, 35

R(3,3,3,4) > 86:

Color 1:  1,  4, 14, 16, 25, 27, 37, 40
Color 2:  5,  6,  7,  8, 17, 18, 19, 20, 29, 30, 31, 32, 41, 42, 43
Color 3:  2,  9, 10, 22, 23, 35, 36, 39
Color 4:  3, 11, 12, 13, 15, 21, 24, 26, 28, 33, 34, 38

Geoff Exoo