# Counterexamples to Hedetniemi's conjecture

## TL;DR

This paper presents counterexamples to Hedetniemi's conjecture, showing that the chromatic number of the product of two graphs can be less than the minimum of their individual chromatic numbers.

## Contribution

It provides the first known counterexamples to Hedetniemi's conjecture, challenging a long-standing assumption in graph theory.

## Key findings

- Counterexamples where $ ext{chromatic}(G imes H) < ext{min}( ext{chromatic}(G), ext{chromatic}(H))$
- Demonstrates the conjecture does not hold universally
- Implications for graph coloring theory and related problems

## Abstract

The chromatic number of $G\times H$ can be smaller than the minimum of the chromatic numbers of finite simple graphs $G$ and $H$.