The two coloring of the edges of K51 which established the lower bound is available as a 0-1 adjacency matrix in which color 0 is K3-free and color 1 is K12-free.
The adjacency matrix is made from six circulant matrices as follows. Due typographical limitations, we use X' to denote X transpose.
| B E G |
A = | E' C F |
| G' F' D |
where
B = (7 8 9 10) C = (2 6 11 15) D = (1 4 13 16) E = (2 3 15 16) F = (2 7 12) G = (2 13 16)
Geoff Exoo