A counterexample to a conjecture on facial unique-maximal colorings

dc.contributor.author Lidicky, Bernard
dc.contributor.author Messerschmidt, Kacy
dc.contributor.author Lidicky, Bernard
dc.contributor.author Skrekovski, Riste
dc.contributor.department Mathematics
dc.date 2018-10-29T21:16:36.000
dc.date.accessioned 2020-06-30T06:00:16Z
dc.date.available 2020-06-30T06:00:16Z
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 proper vertex coloring by natural numbers where on each face α the maximal color appears exactly once on the vertices of α. Fabrici and Göring [4] proved that six colors are enough for any plane graph and conjectured that four colors suffice. This conjecture is a strengthening of the Four Color theorem. Wendland [6] later decreased the upper bound from six to five. In this note, we disprove the conjecture by giving an infinite family of counterexamples. s we conclude that facial unique-maximum chromatic number of the sphere is five.</p>
dc.description.comments <p>This is a manuscript of an article published as Lidický, Bernard, Kacy Messerschmidt, and Riste Škrekovski. "A counterexample to a conjecture on facial unique-maximal colorings." <em>Discrete Applied Mathematics</em> 237 (2018): 123-125. doi: <a href="https://doi.org/10.1016/j.dam.2017.11.037" target="_blank" title="Persistent link using digital object identifier">10.1016/j.dam.2017.11.037</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/190/
dc.identifier.articleid 1192
dc.identifier.contextkey 13191411
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/190
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54580
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/190/2018_Lidicky_CounterexampleConjecture.pdf|||Fri Jan 14 21:51:27 UTC 2022
dc.source.uri 10.1016/j.dam.2017.11.037
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.disciplines Mathematics
dc.subject.keywords facial unique-maximum coloring
dc.subject.keywords plane graph
dc.title A counterexample to a conjecture on facial unique-maximal colorings
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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