The minimum degree of minimal Ramsey graphs for cliques
John Bamberg (University of Western Australia)
Anurag Bishnoi (TU Delft - Discrete Mathematics and Optimization)
Thomas Lesgourgues (University of New South Wales)
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Abstract
We prove that (Formula presented.), where (Formula presented.) is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which is defined as the smallest minimum degree of a graph (Formula presented.) such that any (Formula presented.) -colouring of the edges of (Formula presented.) contains a monochromatic (Formula presented.), whereas no proper subgraph of (Formula presented.) 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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