Lower Bounds for R(5,t)

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'  B
The 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
10 140 35(1,7,11,16)
11 152 38(1,4,11,13,19)
12 180 45(3,10,11,12,16)
13 192 48(5,6,8,15,22,24)
14 220 55(3,7,11,12,13,27)
15 236 59(3,9,11,15,16,21)

Geoff Exoo