3-uniform hypergraphs with no linear cycles

Ervin Gyori

Renyi Institute

Abstract

We explore properties of 3-uniform hypergraphs H without linear cycles. We show that they are at most 3-chromatic, have at least two vertices of strong degree at most two and have independent sets of size at least 2|V(H)|/5.

The talk is based on joint work with A. Gyarfas, and M. Simonovits.