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Coloring Complete and Complete Bipartite Graphs from Random ListsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 32, no 2, 533-542 p.Article in journal (Refereed) PublishedText
##### Abstract [en]

##### Place, publisher, year, edition, pages

SPRINGER JAPAN KK , 2016. Vol. 32, no 2, 533-542 p.
##### Keyword [en]

List coloring; Random list; Coloring from random lists; Complete graph; Complete bipartite graph
##### National Category

Discrete Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-126248DOI: 10.1007/s00373-015-1587-5ISI: 000371081000007OAI: oai:DiVA.org:liu-126248DiVA: diva2:913454
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Available from: 2016-03-21 Created: 2016-03-21 Last updated: 2016-05-27

Assign to each vertex v of the complete graph on n vertices a list L(v) of colors by choosing each list independently and uniformly at random from all f(n)-subsets of a color set , where f(n) is some integer-valued function of n. Such a list assignment L is called a random (f(n), [n])-list assignment. In this paper, we determine the asymptotic probability (as ) of the existence of a proper coloring of , such that for every vertex v of . We show that this property exhibits a sharp threshold at . Additionally, we consider the corresponding problem for the line graph of a complete bipartite graph with parts of size m and n, respectively. We show that if , , and L is a random (f(n), [n])-list assignment for the line graph of , then with probability tending to 1, as , there is a proper coloring of the line graph of with colors from the lists.

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