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Colouring of plane graphs with unique maximal colours on faces
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Wendland, Alex (2016) Colouring of plane graphs with unique maximal colours on faces. Journal of Graph Theory, 83 (4). pp. 359-371. doi:10.1002/jgt.22002 ISSN 0364-9024.
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Official URL: http://dx.doi.org/10.1002/jgt.22002
Abstract
The Four Color Theorem asserts that the vertices of every plane graph can be properly colored with four colors. Fabrici and Göring conjectured the following stronger statement to also hold: the vertices of every plane graph can be properly colored with the numbers 1, …, 4 in such a way that every face contains a unique vertex colored with the maximal color appearing on that face. They proved that every plane graph has such a coloring with the numbers 1, …, 6. We prove that every plane graph has such a coloring with the numbers 1, …, 5 and we also prove the list variant of the statement for lists of sizes seven.
| 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): | Maps , Graph theory, Guthrie, Francis 1831-1899, Appel, Kenneth I., 1932-2013, Haken, Wolfgang | ||||||||||
| Journal or Publication Title: | Journal of Graph Theory | ||||||||||
| Publisher: | John Wiley & Sons Ltd. | ||||||||||
| ISSN: | 0364-9024 | ||||||||||
| Official Date: | December 2016 | ||||||||||
| Dates: |
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| Volume: | 83 | ||||||||||
| Number: | 4 | ||||||||||
| Number of Pages: | 1 | ||||||||||
| Page Range: | pp. 359-371 | ||||||||||
| DOI: | 10.1002/jgt.22002 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||
| Date of first compliant deposit: | 31 May 2016 | ||||||||||
| Date of first compliant Open Access: | 18 November 2016 | ||||||||||
| Funder: | University of Warwick Undergraduate Research Support Scheme, Czech Science Foundation (CSF) | ||||||||||
| Grant number: | GA14-19503S (CSF) | ||||||||||
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| Open Access Version: |
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