R(3,12) > 51

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