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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
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Official URL: http://dx.doi.org/10.1016/j.jctb.2018.03.001
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 | |||||||||||||||
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| 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: |
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| 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 | |||||||||||||||
| RIOXX Funder/Project Grant: |
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