Critical circulant Ramsey graphs

Here, some critical Ramsey graphs with circulant adjacency matrix are shown. The binary string below the figures corresponds to the first row of the circulant adjacency matrix (the asterix indicates the diagonal element).

Please click on the figures to see larger ones.

R(3,3) = 6, i.e., no red 3-cliques, no blue 3-cliques


*0110	*1001

R(3,4) = 9, i.e., no red 3-cliques, no blue 4-cliques


*0110110	*1100011

R(3,5) = 14, i.e., no red 3-cliques, no blue 5-cliques


*011101101110	*100111111001	*111010010111

R(3,6) > 16, i.e., no red 3-cliques, no blue 6-cliques

No critical circulant Ramsey graphs exist.

R(3,7) > 21, i.e., no red 3-cliques, no blue 7-cliques

No critical circulant Ramsey graphs exist.

R(3,8) > 26, i.e., no red 3-cliques, no blue 8-cliques

No critical circulant Ramsey graphs exist.

R(3,9) = 36, i.e., no red 3-cliques, no blue 9-cliques


*1110100101111111111111111010010111	*1001111111110011111100111111111001	*0111110111011110110111101110111110	*1111111011101011001101011101111111

R(4,4) = 18, i.e., no red 4-cliques, no blue 4-cliques


*0010111001110100	*1101000110001011

R(4,5) = 25, i.e., no red 4-cliques, no blue 5-cliques


*00101110011111001110100	*10001110110101101110001	*11000110101110101100011	*11101100001110000110111