Improved Lower Bounds on the Classical Ramsey Numbers R(4,22) and R(4,25)

Madison Lindsay; John W. Cain

Improved Lower Bounds on the Classical Ramsey Numbers R(4,22) and R(4,25)

Combinatorics 2015-10-22 v1

Authors: Madison Lindsay , John W. Cain

Abstract

Circulant graphs have been used to effectively establish lower bounds on many classical Ramsey numbers. Here, we construct circulant graphs of prime order that sharpen the best published lower bounds on two Ramsey numbers. Generalizing previous work in which quadratic and cubic residues were used to construct circulant graphs for the same purpose, we report on the use of quartic and higher-order residues.

Keywords

classical Ramsey numbers lower bounds circulant graphs prime order quadratic residues cubic residues quartic residues

Cite

@article{arxiv.1510.06102,
  title  = {Improved Lower Bounds on the Classical Ramsey Numbers R(4,22) and R(4,25)},
  author = {Madison Lindsay and John W. Cain},
  journal= {arXiv preprint arXiv:1510.06102},
  year   = {2015}
}

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5 pages, 1 figure

Improved Lower Bounds on the Classical Ramsey Numbers R(4,22) and R(4,25)

Abstract

Keywords

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