Computation of the Ramsey Number $R(W_5,K_5)$

Joshua Stinehour; Stanisław Radziszowski; Kung-Kuen Tse

Computation of the Ramsey Number $R(W_5,K_5)$

Discrete Mathematics 2014-05-30 v1

Authors: Joshua Stinehour , Stanisław Radziszowski , Kung-Kuen Tse

Abstract

We determine the value of the Ramsey number $R(W_5,K_5)$ to be 27, where $W_5 = K_1 + C_4$ is the 4-spoked wheel of order 5. This solves one of the four remaining open cases in the tables given in 1989 by George R. T. Hendry, which included the Ramsey numbers $R(G,H)$ for all pairs of graphs $G$ and $H$ having five vertices, except seven entries. In addition, we show that there exists a unique up to isomorphism critical Ramsey graph for $W_5$ versus $K_5$ . Our results are based on computer algorithms.

Keywords

Ramsey number wheel graph complete graph critical graph computer algorithms

Cite

@article{arxiv.cs/0512044,
  title  = {Computation of the Ramsey Number $R(W_5,K_5)$},
  author = {Joshua Stinehour and Stanisław Radziszowski and Kung-Kuen Tse},
  journal= {arXiv preprint arXiv:cs/0512044},
  year   = {2014}
}

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5 pages

Computation of the Ramsey Number $R(W_5,K_5)$

Abstract

Keywords

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