The ACO Seminar (2025–2026)

The Ramsey number R(t,k) is the smallest n such that any red-blue edge coloring of the n-vertex complete graph has either a t-vertex red complete subgraph or a k-vertex blue complete subgraph. We will investigate the history of asymptotic bounds on the extreme off-diagonal Ramsey numbers R(3,k) and present a new lower bound that has been conjectured to be asymptotically tight.