The University College London (UCL) Combinatorics Seminar takes place weekly on Mondays, from 4pm to 5pm, at 20 Bedford Way (IOE Bulding) Room 828. It is organised by Shoham Letzter and Alexey Pokrovskiy.

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Next Speaker

• 10 May 2022 - Anurag Bishnoi (UCL)

  The minimum degree of minimal Ramsey graphs for cliques

  
  

  We will present a new upper bound of $s_r(K_k) = O(k^5 r^{5/2})$ on the Ramsey parameter $s_r(K_k)$ introduced by Burr, Erdős and Lovász 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. This improves the previous upper bound of $s_r(K_k) = O(k^6 r^3)$ proved by Fox et al. The construction used in our proof relies on a group theoretic model of generalised quadrangles introduced by Kantor in 1980.

  This is joint work with John Bamberg and Thomas Lesgourgues.