# Zero-free intervals of chromatic polynomials of mixed hypergraphs

## TL;DR

This paper establishes new zero-free intervals for chromatic polynomials of certain hypergraph families, extending known results from graphs to hypergraphs and identifying specific intervals where these polynomials do not have zeros.

## Contribution

It proves zero-free intervals for chromatic polynomials of hypergraphs, generalizing previous graph results and identifying specific intervals for hypergraph families.

## Key findings

- (-∞, 0) is zero-free for hypergraph chromatic polynomials
- (0, 1) is zero-free for a subfamily of hypergraphs
- Extends known graph zero-free results to hypergraphs

## Abstract

In this paper, we prove that $(-\infty, 0)$ is a zero-free interval for chromatic polynomials of a family ${\cal L}_0$ of hypergraphs and $(0, 1)$ is a zero-free interval for chromatic polynomials of a subfamily ${\cal L}_0'$ of ${\cal L}_0$ of hypergraphs. These results extend known results on zero-free intervals of chromatic polynomials of graphs and hypergraphs.