The ACO Seminar (2023–2024)

Erdos and Gyarfas (1997) investigated the following parameter that generalizes classical Ramsey numbers: let f(n,p,q) be the minimum number of colors required to color the edges of an n-clique such that every p-subclique receives at least q colors. This parameter has led to many interesting problems. I will show how a recent generalization of an old result of Frankl and Rodl about hypergraph matchings can be used to settle some cases of the Erdos-Gyarfas problem by giving asymptotically optimal constructions. This is joint work with Felix Joos.