Computing the Ramsey Number $R(K_5-P_3,K_5)$
Combinatorics
2014-05-29 v1 Discrete Mathematics
Abstract
We give a computer-assisted proof of the fact that . This solves one of the three remaining open cases in Hendry's table, which listed the Ramsey numbers for pairs of graphs on 5 vertices. We find that there exist no -good graphs containing a on 23 or 24 vertices, where a graph is -good if does not contain and the complement of does not contain . The unique -good graph containing a on 22 vertices is presented.
Keywords
Cite
@article{arxiv.1203.6536,
title = {Computing the Ramsey Number $R(K_5-P_3,K_5)$},
author = {Jesse A. Calvert and Michael J. Schuster and Stanisław P. Radziszowski},
journal= {arXiv preprint arXiv:1203.6536},
year = {2014}
}