On facial unique-maximum (edge-)coloring

dc.contributor.author Andova, Vesna
dc.contributor.author Lidicky, Bernard
dc.contributor.author Luzar, Borut
dc.contributor.author Skrekovski, Riste
dc.contributor.department Mathematics
dc.date 2018-10-29T21:15:05.000
dc.date.accessioned 2020-06-30T06:00:15Z
dc.date.available 2020-06-30T06:00:15Z
dc.date.copyright Sun Jan 01 00:00:00 UTC 2017
dc.date.issued 2018-03-11
dc.description.abstract <p>A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face α the maximal color appears exactly once on the vertices of α. If the coloring is required to be proper, then the upper bound for the minimal number of colors required for such a coloring is set to 5. Fabrici and Göring [5] even con- jectured that 4 colors always suffice. Confi the conjecture would hence give a considerable strengthening of the Four Color Theorem. In this paper, we prove that the conjecture holds for subcubic plane graphs, outerplane graphs and plane quadrangulations. Additionally, we consider the facial edge-coloring analogue of the aforementioned coloring and prove that every 2-connected plane graph admits such a coloring with at most 4 colors.</p>
dc.description.comments <p>This is a manuscript of an article pulblished as Andova, Vesna, Bernard Lidický, Borut Lužar, and Riste Škrekovski. "On facial unique-maximum (edge-) coloring." <em>Discrete Applied Mathematics</em> 237 (2018): 26-32. doi: <a href="https://doi.org/10.1016/j.dam.2017.11.024" target="_blank" title="Persistent link using digital object identifier">10.1016/j.dam.2017.11.024</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/189/
dc.identifier.articleid 1193
dc.identifier.contextkey 13192186
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/189
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54578
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/189/2018_Lidicky_FacialUnique.pdf|||Fri Jan 14 21:47:39 UTC 2022
dc.source.uri 10.1016/j.dam.2017.11.024
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.disciplines Mathematics
dc.subject.keywords facial unique-maximum coloring
dc.subject.keywords facial unique-maximum edge-coloring
dc.subject.keywords plane graph
dc.title On facial unique-maximum (edge-)coloring
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication a1d8f5ab-9124-4104-981c-8ba1e426e3ff
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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