Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

7-2017

Journal or Book Title

Graphs and Combinatorics

Volume

33

Issue

4

First Page

751

Last Page

787

DOI

10.1007/s00373-017-1812-5

Abstract

All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any ℓ ∈ {3, 4, 5, 6, 7}, a planar graph is 4-choosable if it is ℓ-cycle-free. In terms of constraining the list assignment, one refinement of k-choosability is choosability with separation. A graph is (k, s)-choosable if the graph is colorable from lists of size k where adjacent vertices have at most s common colors in their lists. Every planar graph is (4, 1)-choosable, but there exist planar graphs that are not (4, 3)-choosable. It is an open question whether planar graphs are always (4, 2)-choosable. A chorded ℓ-cycle is an ℓ-cycle with one additional edge. We demonstrate for each ℓ ∈ {5, 6, 7} that a planar graph is (4, 2)-choosable if it does not contain chorded ℓ-cycles.

Comments

This is a pre-print of an article published in Graphs and Combinatorics. The final authenticated version is available online at doi: 10.1007/s00373-017-1812-5.

Copyright Owner

Springer Japan

Language

en

File Format

application/pdf

Published Version

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