Dylan King : R(3,k) in two bites

Posted by Vishesh Jain , part of the Mathematical Computer Science Seminar.

At

April 13, 2026, 3 p.m.

In

1227 SEO

Abstract

The triangle Ramsey number R(3,k) is the smallest n such that any n-vertex graph contains either a triangle or an independent set of size k. Through the hard work of many researchers, around 30 years ago the order of magnitude of R(3,k) was determined to be k^2/log(k), and the correct leading constant is now of serious interest. The main result of this talk improves the best known lower bound on this constant from 1/2 to 1/3, using a flexible construction. Based on joint work with Zion Hefty, Paul Horn, and Florian Pfender.