- Series
- Combinatorics Seminar
- Time
- Friday, February 19, 2021 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke
- Speaker
- Anurag Bishnoi – TU Delft – https://anuragbishnoi.wordpress.com/
- Organizer
- Lutz Warnke
We prove 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, 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 $K_k$, 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.
Talk based on https://arxiv.org/abs/2008.02474