A New Lower Bound for the Ramsey Number R(4, 8)
Discrete Mathematics
2013-04-02 v3 Combinatorics
Abstract
The lower bound for the classical Ramsey number R(4, 8) is improved from 56 to 58. The author has found a new edge coloring of K_{57} that has no complete graphs of order 4 in the first color, and no complete graphs of order 8 in the second color. The coloring was found using a SAT solver which is based on MiniSat and customized for solving Ramsey problems.
Cite
@article{arxiv.1212.1328,
title = {A New Lower Bound for the Ramsey Number R(4, 8)},
author = {Hiroshi Fujita},
journal= {arXiv preprint arXiv:1212.1328},
year = {2013}
}