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Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk

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Dvořák, Zdeněk, Králʼ, Daniel and Thomas, Robin (2018) Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk. Journal of Combinatorial Theory Series B, 132 . pp. 1-46. doi:10.1016/j.jctb.2018.03.001 ISSN 0095-8956.

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Official URL: http://dx.doi.org/10.1016/j.jctb.2018.03.001

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Abstract

Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring of a cycle C of G that does not extend to a 3-coloring of G, then G has a subgraph H on O(|C|) vertices that also has no 3-coloring extending. This is asymptotically best possible and improves a previous bound of Thomassen. In the next paper of the series we will use this result and the attendant theory to prove a generalization to graphs on surfaces with several precolored cycles.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Graph coloring
Journal or Publication Title: Journal of Combinatorial Theory Series B
Publisher: Elsevier
ISSN: 0095-8956
Official Date: September 2018
Dates:
DateEvent
September 2018Published
27 March 2018Available
3 March 2018Accepted
Volume: 132
Page Range: pp. 1-46
DOI: 10.1016/j.jctb.2018.03.001
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 5 March 2018
Date of first compliant Open Access: 27 March 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
GACR 201/09/0197 Grantová Agentura České Republikyhttp://dx.doi.org/10.13039/501100001824
P202/12/G061Grantová Agentura České Republikyhttp://dx.doi.org/10.13039/501100001824
DMS-0739366 National Science Foundationhttp://dx.doi.org/10.13039/100000001
DMS-1202640National Science Foundationhttp://dx.doi.org/10.13039/100000001
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