Asymptotic Normality of the Chromatic Number of a Random Graph

TL;DR

This paper proves that the distribution of the chromatic number of a random graph converges to a normal distribution as the number of vertices increases, after proper normalization.

Contribution

It establishes the asymptotic normality of the chromatic number for fixed edge probability in random graphs, a significant theoretical advancement.

Findings

Chromatic number distribution converges to Normal as n increases

Provides a rigorous proof of asymptotic normality for fixed p

Enhances understanding of graph coloring in probabilistic models

Abstract

In this paper we prove that the limiting distribution of the Chromatic number of a random graph $\mathcal{G}_{n,p}$, with fixed edge-probability $p$, after appropriate centering and scaling is Normal, when the number of vertices $n$, goes to infinity.