Construct a circulant graph on 184 vertices with vertices labeled with 0 to 183. For i > j, the edge joining i and j is colored in the first color if either i - j or 183 - (i - j) is one of the following values:

5, 7, 12, 14, 16, 17, 18, 19, 21, 23, 25, 27, 33, 34, 35, 36, 39, 40 42, 45, 47, 49, 50, 57, 61, 64, 68, 73, 75, 78, 79, 83, 84, 86, 89, 92

Otherwise the edge receives color two.
There are no K_{6}'s in the first color and
no K_{10}'s in the second color.

Geoff Exoo