The Alon-Tarsi number of planar graphs -- a simple proof

TL;DR

This paper presents a simplified proof that all planar graphs have an Alon-Tarsi number at most 5, and identifies a matching that reduces the Alon-Tarsi number of the remaining graph to at most 4.

Contribution

It provides a straightforward proof of the Alon-Tarsi number bounds for planar graphs and introduces a matching that improves the bound.

Findings

Every planar graph has Alon-Tarsi number ≤ 5

Existence of a matching reducing the Alon-Tarsi number to ≤ 4 after removal

Simplified proof technique for Alon-Tarsi bounds on planar graphs

Abstract

This paper gives a simple proof of the result that every planar graph $G$ has Alon-Tarsi number at most 5, and has a matching $M$ such that $G-M$ has Alon-Tarsi number at most 4.