The two coloring of the edges of
K_{51} which established the lower bound is
available as a 0-1
adjacency matrix
in which color 0 is K_{3}-free and color 1
is K_{12}-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