The ACO Seminar (2025–2026)

A conjecture of Alon states that, for some absolute constant C, every finite group G possesses a Cayley graph with clique and independence number each at most C*log|G|. Recently, Conlon, Fox, Pham, and Yepremyan have verified this conjecture for most abelian groups using mainly graph-theoretic techniques. In this talk, I will discuss some recent work of mine extending their results to many non-abelian groups. In addition to combinatorial inputs from Conlon--Fox--Pham--Yepremyan, the techniques used are inspired by additive combinatorics and expansion in groups.