Maffray, F, Penev, I and Vušković, K (2021) Coloring Rings. Journal of Graph Theory, 96 (4). pp. 642-683. ISSN 0364-9024
Abstract
A ring is a graph whose vertex set can be partitioned into nonempty sets, , such that for all , the set can be ordered as so that . A hyperhole is a ring such that for all , is complete to . In this paper, we prove that the chromatic number of a ring is equal to the maximum chromatic number of a hyperhole in . Using this result, we give a polynomial-time coloring algorithm for rings. Rings formed one of the basic classes in a decomposition theorem for a class of graphs studied by Boncompagni et al [J. Graph Theory 91 (2019), 192–246.]. Using our coloring algorithm for rings, we show that graphs in this larger class can also be colored in polynomial time. Furthermore, we find the optimal -bounding function for this larger class of graphs, and we also verify Hadwiger's conjecture for it.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Wiley Periodicals LLC. This is the peer reviewed version of the following article: Maffray, F, Penev, I and Vušković, K (2020) Coloring Rings. Journal of Graph Theory. ISSN 0364-9024, which has been published in final form at https://doi.org/10.1002/jgt.22635. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. |
Keywords: | algorithms; chromatic number; Hadwiger's conjecture; optimal χ‐bounding function; vertex coloring |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/N019660/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Oct 2020 12:02 |
Last Modified: | 23 Nov 2023 15:08 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/jgt.22635 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:151594 |