Corpus ID: 221005988

The minimum degree of minimal Ramsey graphs for cliques.

@article{Bamberg2020TheMD,
  title={The minimum degree of minimal Ramsey graphs for cliques.},
  author={John Bamberg and Anurag Bishnoi and Thomas Lesgourgues},
  journal={arXiv: Combinatorics},
  year={2020}
}
We prove that $s_r(K_k) = O(k^5 r^{5/2})$, where $s_r(K_k)$ is the Ramsey parameter introduced by Burr, Erdős and Lovasz in 1976, which is defined as the smallest minimum degree of a graph $G$ such that any $r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no proper subgraph of $G$ has this property. The construction used in our proof relies on a group theoretic model of generalised quadrangles introduced by Kantor in 1980. 

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