K.K. Dabrowski
Filling the complexity gaps for colouring planar and bounded degree graphs
Dabrowski, K.K.; Dross, F.; Johnson, M.; Paulusma, D.
Authors
F. Dross
Professor Matthew Johnson matthew.johnson2@durham.ac.uk
Head Of Department
Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
Abstract
A colouring of a graphGVE=( ,)is a function→cV:{1, 2,...}such that≠cucv() ()for every∈uvE.Ak‐regular list assignment ofGis a functionLwith domainVsuch that for every∈uV,Lu()is asubset of{1, 2,...}of sizek. A colouringcofGrespects ak‐regular list assignmentLofGif∈cuLu() ()forevery∈uV. A graphGisk‐choosable if for everyk‐regular list assignmentLofG, there exists a colouringofGthat respectsL. We may also ask if for a givenk‐regular list assignmentLof a given graphG, thereexists a colouring ofGthat respectsL. This yields thek‐REGULARLISTCOLOURINGproblem. For∈k{3, 4},wedetermine a family of classeseof planar graphs, suchthat eitherk‐REGULARLISTCOLOURINGisNP‐complete forinstancesGL(,)withe∈G, or everye∈Gisk‐choosable. By using known examples of non‐3‐choosable and non‐4‐choosable graphs, this enables usto classify the complexity ofk‐REGULARLISTCOLOURINGrestricted to planar graphs, planar bipartite graphs,planar triangle‐free graphs, and planar graphs with no4‐cycles and no5‐cycles. We also classify the complexityofk‐REGULARLISTCOLOURINGand a number of relatedcolouring problems for graphs with bounded maximumdegree.
Citation
Dabrowski, K., Dross, F., Johnson, M., & Paulusma, D. (2019). Filling the complexity gaps for colouring planar and bounded degree graphs. Journal of Graph Theory, 92(4), 377-393. https://doi.org/10.1002/jgt.22459
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 14, 2019 |
Online Publication Date | May 31, 2019 |
Publication Date | Dec 1, 2019 |
Deposit Date | Mar 15, 2019 |
Publicly Available Date | Mar 28, 2024 |
Journal | Journal of Graph Theory |
Print ISSN | 0364-9024 |
Electronic ISSN | 1097-0118 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 92 |
Issue | 4 |
Pages | 377-393 |
DOI | https://doi.org/10.1002/jgt.22459 |
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Copyright Statement
This is the accepted version of the following article: Dabrowski, K.K., Dross, F., Johnson, M. & Paulusma, D. (2019). Filling the complexity gaps for colouring planar and bounded degree graphs. Journal of Graph Theory 92(4): 377-393., which has been published in final form at https://doi.org/10.1002/jgt.22459. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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