English

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 R(K5P3,K5)=25R(K_5-P_3, K_5)=25. 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 (K5P3,K5)(K_5-P_3,K_5)-good graphs containing a K4K_4 on 23 or 24 vertices, where a graph FF is (G,H)(G,H)-good if FF does not contain GG and the complement of FF does not contain HH. The unique (K5P3,K5)(K_5-P_3,K_5)-good graph containing a K4K_4 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}
}
R2 v1 2026-06-21T20:41:51.919Z