Computation of the Ramsey Number $R(W_5,K_5)$
<|reference_start|>Computation of the Ramsey Number $R(W_5,K_5)$: 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.<|reference_end|>
@article{stinehour2005computation,
    title={Computation of the Ramsey Number $R(W_5,K_5)$},
    author={Joshua Stinehour, Stanis{l}aw Radziszowski and Kung-Kuen Tse},
    journal={Bulletin of the Institute of Combinatorics and Its Applications,
  47 (2006) 53-57},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0512044},
    primaryClass={cs.DM}
}