Random constructions of hypergraphs with large girth and without panchromatic colorings

A. E. Khuzieva

Moscow Institute of Physics and Technology, Moscow, Russia

Abstract: We give probabilistic constructions of hypergraphs with large girth that do not admit panchromatic colorings. We prove new upper bounds on the minimal values of the number of edges and the maximum vertex degree in such hypergraphs.

UDC: 519.179.1+519.174

 English version: Journal of Mathematical Sciences (New York), 2022, 262:4, 581–590