Improving $R(3,k)$ in just two bites

Series
Combinatorics Seminar
Time
Friday, January 23, 2026 - 3:15pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Florian Pfender – University of Colorado Denver – FLORIAN.PFENDER@UCDENVER.EDUhttps://sites.google.com/view/florianpfendermath
Organizer
Jiaxi Nie

We present a random construction proving that the extreme off-diagonal Ramsey numbers satisfy $R(3,k)\ge  \left(\frac12+o(1)\right)\frac{k^2}{\log{k}}$ (conjectured to be asymptotically tight), improving the previously best bound $R(3,k)\ge  \left(\frac13+o(1)\right)\frac{k^2}{\log{k}}$. In contrast to all previous constructions achieving the correct order of magnitude, we do not use a nibble argument.

Beyond the paper, we will explore a bit further how the approach can be used for other problems.