## PIMS - SFU Discrete Math Seminar: Anurag Bishnoi

• Date: 07/28/2021
• Time: 10:30
Lecturer(s):
Anurag Bishnoi, TU Delft
Location:

Online

Topic:

The Minimum Degree of Minimal Ramsey Graphs for Cliques

Description:

Abstract: In this talk we will present a new upper bound of $s_r(K_t) = O(t^5r^{5/2})$ on the Ramsey parameter $s_r(K_t)$ introduced by Burr, Erd\H{o}s and Lov\'{a}sz 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_t$, whereas no proper subgraph of$G$has this property. This improves the previous upper bound of$s_r(K_t) = O(t^6r^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 (https://arxiv.org/abs/2008.02474).

Other Information: