The colorings that improve the lower bounds for R(5,t), 10 <= t <= 15, are constructed by the same method. In each case we begin with the adjacency matrix B of a (3,t-1)-coloring. and let C be the adjacency matrix of the coloring complementary to B. Both B and C have color 1 on the main diagonal. Each of the (5,t)-colorings has an adjacency matrix with the following form (where we use X' to denote X-transpose):
B C B B C' B B B B' B' B C B' B' C' BThe complete the constructions, we need to specify the (3,t-1)-colorings that we are using to determine B. These are all circle colorings and are given in the table below.
|t||Number of vertices||(3,t-1)-coloring used|