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Some results on cyclic interval edge colorings of graphs
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Yerevan State University, Armenia; National Academic Science, Armenia.
2018 (English)In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 87, no 2, p. 239-252Article in journal (Refereed) Published
Abstract [en]

A proper edge coloring of a graph G with colors 1,2,,t is called a cyclic interval t-coloring if for each vertex v of G the edges incident to v are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t. We prove that a bipartite graph G of even maximum degree (G)4 admits a cyclic interval (G)-coloring if for every vertex v the degree dG(v) satisfies either dG(v)(G)-2 or dG(v)2. We also prove that every Eulerian bipartite graph G with maximum degree at most eight has a cyclic interval coloring. Some results are obtained for (a,b)-biregular graphs, that is, bipartite graphs with the vertices in one part all having degree a and the vertices in the other part all having degree b; it has been conjectured that all these have cyclic interval colorings. We show that all (4, 7)-biregular graphs as well as all (2r-2,2r)-biregular (r2) graphs have cyclic interval colorings. Finally, we prove that all complete multipartite graphs admit cyclic interval colorings; this proves a conjecture of Petrosyan and Mkhitaryan.

Place, publisher, year, edition, pages
WILEY , 2018. Vol. 87, no 2, p. 239-252
Keyword [en]
bipartite graph; biregular graph; complete multipartite graph; cyclic interval coloring; edge coloring; interval coloring
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-143883DOI: 10.1002/jgt.22154ISI: 000417854500008OAI: oai:DiVA.org:liu-143883DiVA: diva2:1170091
Note

Funding Agencies|Armenian National Science and Education Fund (ANSEF) based in New York, USA

Available from: 2018-01-02 Created: 2018-01-02 Last updated: 2018-02-01

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The full text will be freely available from 2018-05-30 12:31
Available from 2018-05-30 12:31

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