The minimum degree of minimal Ramsey graphs for cliques
John Bamberg, Anurag Bishnoi, Thomas Lesgourgues

TL;DR
This paper establishes an upper bound on the minimum degree of minimal Ramsey graphs for cliques using a group-theoretic construction, advancing understanding of the structural properties of such graphs.
Contribution
It provides a new upper bound on the Ramsey parameter for cliques, employing a novel group-theoretic approach with generalized quadrangles.
Findings
Proves that s_r(K_k) = O(k^5 r^{5/2})
Uses a group-theoretic model of generalized quadrangles
Advances bounds on minimal Ramsey graphs for cliques
Abstract
We prove that , where is the Ramsey parameter introduced by Burr, Erd\H{o}s and Lov\'{a}sz in 1976, which is defined as the smallest minimum degree of a graph such that any -colouring of the edges of contains a monochromatic , whereas no proper subgraph of 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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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory
