The minimum degree of minimal Ramsey graphs for cliques

John Bamberg, Anurag Bishnoi, Thomas Lesgourgues

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1827-1838
Number of pages12
JournalBulletin of the London Mathematical Society
Issue number5
Early online date15 Apr 2022
Publication statusPublished - Oct 2022


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