Coloring cross-intersecting families

TL;DR

This paper explores coloring problems in cross-intersecting families within extremal combinatorics, extending classical hypergraph coloring concepts to a specialized class of hypergraphs.

Contribution

It addresses coloring problems for cross-intersecting families, building on Erdős and Lovász's work, and provides new insights into hypergraph coloring restrictions.

Findings

Analyzed coloring constraints for cross-intersecting families

Extended classical hypergraph coloring results to a new family class

Provided solutions or bounds for coloring problems in this context

Abstract

Intersecting and cross-intersecting families usually appear in extremal combinatorics in the vein of the Erd{\H o}s--Ko--Rado theorem. On the other hand, P.~Erd{\H o}s and L.~Lov{\'a}sz in the noted paper~\cite{EL} posed problems on coloring intersecting families as a restriction of classical hypergraph coloring problems to a special class of hypergraphs. This note deals with the mentioned coloring problems stated for cross-intersecting families.