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On interval and cyclic interval edge colorings of (3,5)-biregular graphs
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Yerevan State University, Armenia.
University of Southern Denmark, Denmark.
2017 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 340, no 11, 2678-2687 p.Article in journal (Refereed) Published
Abstract [en]

A proper edge coloring f of a graph G with colors 1, 2, 3, . . . , t is called an interval coloring if the colors on the edges incident to every vertex of G form an interval of integers. The coloring f is cyclic interval if for every vertex v of G, the colors on the edges incident to v either form an interval or the set {1, . . . t} \ {f (e) : e is incident to v} is an interval. A bipartite graph G is (a, b)-biregular if every vertex in one part has degree a and every vertex in the other part has degree b; it has been conjectured that all such graphs have interval colorings. We prove that every (3, 5)-biregular graph has a cyclic interval coloring and we give several sufficient conditions for a (3, 5)-biregular graph to admit an interval coloring. (C) 2016 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2017. Vol. 340, no 11, 2678-2687 p.
Keyword [en]
Interval edge coloring; Biregular graph; Cyclic interval edge coloring; Edge coloring
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-141695DOI: 10.1016/j.disc.2016.09.020ISI: 000411297200009OAI: oai:DiVA.org:liu-141695DiVA: diva2:1147349
Note

Funding Agencies|SVeFUM

Available from: 2017-10-05 Created: 2017-10-05 Last updated: 2017-10-31

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The full text will be freely available from 2018-09-15 14:12
Available from 2018-09-15 14:12

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Casselgren, Carl Johan
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf