Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8

TL;DR

This paper introduces correspondence coloring, a new graph coloring variant, and proves that planar graphs without cycles of lengths 4 to 8 are 3-choosable, solving a question posed by Borodin.

Contribution

The paper develops correspondence coloring and applies it to establish 3-choosability of certain planar graphs, extending previous coloring techniques.

Findings

Planar graphs without cycles of lengths 4 to 8 are 3-choosable.

Correspondence coloring generalizes list coloring and enables new reductions.

Answer to Borodin's question on cycle length restrictions and graph colorability.

Abstract

We introduce a new variant of graph coloring called correspondence coloring which generalizes list coloring and allows for reductions previously only possible for ordinary coloring. Using this tool, we prove that excluding cycles of lengths 4 to 8 is sufficient to guarantee 3-choosability of a planar graph, thus answering a question of Borodin.