The connection between the chromatic numbers of a hypergraph and its $1$-intersection graph
Combinatorics
2024-06-19 v1
Abstract
A well known problem from an excellent book of Lov\'asz states that any hypergraph with the property that no pair of hyperedges intersect in exactly one vertex can be properly 2-colored. Motivated by this as well as recent works of Keszegh and of Gy\'arf\'as et al we study the -intersection graph of a hypergraph. The -intersection graph encodes those pairs of hyperedges in a hypergraph that intersect in exactly one vertex. We prove for that all hypergraphs whose -intersection graph is -partite can be properly -colored.
Cite
@article{arxiv.2406.12118,
title = {The connection between the chromatic numbers of a hypergraph and its $1$-intersection graph},
author = {Zoltán L. Blázsik and Nathan W. Lemons},
journal= {arXiv preprint arXiv:2406.12118},
year = {2024}
}