Construct a circulant graph on 166 vertices with vertices labeled with 0 to 165. For i > j, the edge joining i and j is colored in the first color if either i - j or 166 - (i - j) is one of the following values:
2, 10, 11, 12, 14, 17, 18, 27, 28, 30
32, 33, 36, 37, 38, 39, 40, 41, 43, 46
48, 51, 55, 57, 59, 61, 62, 68, 69, 72
73, 74, 77, 80, 81
Otherwise the edge receives color two. There are no K6's in the first color and no K10's in the second color.
Geoff Exoo