Relation between the correspondence chromatic number and the Alon--Tarsi number

TL;DR

This paper explores the relationship between the correspondence chromatic number and the Alon--Tarsi number, providing new examples of graphs where these parameters differ, thereby deepening understanding of graph coloring bounds.

Contribution

It introduces a family of graphs with arbitrary Alon--Tarsi number and a correspondence chromatic number exactly one less, illustrating the nuanced relationship between these two bounds.

Findings

Existence of graphs with arbitrary Alon--Tarsi number and correspondence chromatic number one less

Demonstrates that the Alon--Tarsi number can exceed the correspondence chromatic number

Provides insights into bounds on the list chromatic number of graphs

Abstract

We study the relation between the correspondence chromatic number and the Alon--Tarsi number, both upper bounds on the list chromatic number of a graph. There are many graphs with Alon--Tarsi number greater than the correspondence chromatic number. We present here a family of graphs with arbitrary Alon--Tarsi number, with correspondence chromatic number one larger. Keywords: correspondence coloring, Alon--Tarsi number AMS Mathematics Subject Classification: 05C15