# Non-concentration of the chromatic number of a random graph

## TL;DR

This paper demonstrates that the chromatic number of a random graph G_{n, 1/2} is not tightly concentrated on a small set of values, resolving a longstanding open problem in graph theory.

## Contribution

It proves that the chromatic number of G_{n, 1/2} is not concentrated on fewer than n^{1/4 - ε} values, providing new insights into the distribution of chromatic numbers.

## Key findings

- Chromatic number of G_{n, 1/2} is highly dispersed.
- Addresses a longstanding open question by Erdős.
- Shows non-concentration on fewer than n^{1/4 - ε} values.

## Abstract

We show that the chromatic number of $G_{n, \frac 12}$ is not concentrated on fewer than $n^{\frac 14 - \varepsilon}$ consecutive values. This addresses a longstanding question raised by Erd\H{o}s and several other authors.