Ramsey Numbers of Connected Clique Matchings

Barnaby Roberts

Ramsey Numbers of Connected Clique Matchings

Combinatorics 2016-05-25 v1

Authors: Barnaby Roberts

Abstract

We determine the Ramsey number of a connected clique matching. That is, we show that if $G$ is a $2$ -edge-coloured complete graph on $(r^2 - r - 1)n - r + 1$ vertices, then there is a monochromatic connected subgraph containing $n$ disjoint copies of $K_r$ , and that this number of vertices cannot be reduced.

Keywords

Ramsey number connected clique matching edge-coloured complete graph monochromatic connected subgraph disjoint copies of K_r

Cite

@article{arxiv.1605.07492,
  title  = {Ramsey Numbers of Connected Clique Matchings},
  author = {Barnaby Roberts},
  journal= {arXiv preprint arXiv:1605.07492},
  year   = {2016}
}

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