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

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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:	Date Event December 2016 Published 18 November 2015 Available 23 October 2015 Accepted 13 September 2014 Submitted
Date of first compliant deposit:	31 May 2016
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
Funder:	University of Warwick Undergraduate Research Support Scheme, Czech Science Foundation (CSF)
Grant number:	GA14-19503S (CSF)
Adapted As:
Open Access Version:	ArXiv

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