# Edge colorings of graphs without monochromatic stars

## TL;DR

This paper improves bounds on the maximum number of edge colorings of graphs that avoid monochromatic stars, using advanced entropy inequalities to refine previous results.

## Contribution

It introduces an improved application of Shearer's entropy inequality to better estimate edge colorings avoiding monochromatic stars.

## Key findings

- Enhanced bounds on edge colorings without monochromatic stars
- Application of Shearer's entropy inequality to graph coloring problems
- Refinement of previous theoretical results in graph coloring

## Abstract

In this note, we improve on results of Hoppen, Kohayakawa and Lefmann about the maximum number of edge colorings without monochromatic copies of a star of a fixed size that a graph on $n$ vertices may admit. Our results rely on an improved application of an entropy inequality of Shearer.