Correspondence coloring of random graphs

TL;DR

This paper proves that Erdős-Rényi random graphs with constant density have a correspondence chromatic number proportional to n divided by the square root of log n, aligning with a conjecture for correspondence coloring.

Contribution

It establishes an upper bound on the correspondence chromatic number of random graphs, confirming a prediction from linear Hadwiger's conjecture.

Findings

Correspondence chromatic number of G(n,p) is O(n/√log n) for constant p<1.

Provides a simple sufficient condition for correspondence colorability based on independent sets.

Matches the predicted bounds from conjectures in graph theory.

Abstract

We show that Erd\H{o}s-R\'enyi random graphs $G(n,p)$ with constant density $p<1$ have correspondence chromatic number $O(n/\sqrt{\log n})$; this matches a prediction from linear Hadwiger's conjecture for correspondence coloring. The proof follows from a simple sufficient condition for correspondence colorability in terms of the numbers of independent sets.