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The Alon–Tarsi number of planar graphs

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Abstract

This paper proves that the Alon–Tarsi number of any planar graph is at most 5, which solves an open problem posed in Hefetz (2011) [2] and gives an alternate proof of the 5-choosability as well as the 5-paintability of planar graphs.

Keywords

Planar graph
List colouring
On-line list colouring
Alon–Tarsi number

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1

Grant Number: NSFC 11571319.