# Ramsey-Numbers

This site contains the solution graphs which prove new lower bounds for Ramsey Numbers R(m, n) described in the following paper:

Computational new IP-based bounds for small Ramsey Numbres using circulant colorings
by Fabio Furini, Ivana Ljubic and Pablo San Segundo (under review 2021).

Each file provides a circulant 2-coloring of a complete graph in which the size of a largest blue clique is at most m and the size of a largest red clique is at most n. A 0 in row i and column j refers to a red edge with endpoints in vertices i and j. A 1 in row i and column j refers to a blue edge with endpoints in vertices i and j. The order of the graph is provided in the first line of the files.