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Vertex coloring complete multipartite graphs from random lists of size 2
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, no 13, 1150-1157 p.Article in journal (Refereed) Published
Abstract [en]

Let Ks×m be the complete multipartite graph with s parts and m vertices in each part. Assign to each vertex v of Ks×m a list L(v) of colors, by choosing each list uniformly at random from all 2-subsets of a color set C of size σ(m). In this paper we determine, for all fixed s and growing m, the asymptotic probability of the existence of a proper coloring φ, such that φ(v)∈L(v) for all vV(Ks×m). We show that this property exhibits a sharp threshold at σ(m)=2(s−1)m.

Place, publisher, year, edition, pages
2011. Vol. 311, no 13, 1150-1157 p.
Keyword [en]
List coloring; Complete multipartite graph; Random list
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-43323DOI: 10.1016/j.disc.2010.07.013OAI: oai:DiVA.org:umu-43323DiVA: diva2:413020
Available from: 2011-04-27 Created: 2011-04-27 Last updated: 2017-12-11Bibliographically approved
In thesis
1. On some graph coloring problems
Open this publication in new window or tab >>On some graph coloring problems
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för matematik och matematisk statistik, 2011. 22 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 48
Keyword
List coloring, interval edge coloring, coloring graphs from random lists, biregular graph, avoiding arrays, Latin square, scheduling
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-43389 (URN)978-91-7459-198-9 (ISBN)
Public defence
2011-05-20, MIT-huset, MA121, Umeå universitet, Umeå, 13:15
Opponent
Supervisors
Available from: 2011-04-29 Created: 2011-04-28 Last updated: 2011-05-20Bibliographically approved

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Casselgren, Carl Johan

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