A Conjecture of Erdős the Ramsey Number r ( W 6 )

@inproceedings{Faudree1996ACO,
  title={A Conjecture of Erdős the Ramsey Number r ( W 6 )},
  author={Ralph J. Faudree and Brendan D. McKay},
  year={1996}
}
It was conjectured by Paul Erdős that if G is a graph with chromatic number at least k, then the diagonal Ramsey number r(G) ≥ r(Kk). That is, the complete graph Kk has the smallest diagonal Ramsey number among the graphs of chromatic number k. This conjecture is shown to be false for k = 4 by verifying that r(W6) = 17, where W6 is the wheel with 6 vertices, since it is well known that r(K4) = 18. Computational techniques are used to determine r(W6) as well as the Ramsey numbers for other pairs… CONTINUE READING