References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Coloring graphs from random lists of fixed sizePrimeFaces.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}); 2014 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 44, no 3, 317-327 p.Article in journal (Refereed) Published
##### Abstract [en]

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

Wiley , 2014. Vol. 44, no 3, 317-327 p.
##### Keyword [en]

random list; list coloring
##### National Category

Natural Sciences
##### Identifiers

URN: urn:nbn:se:liu:diva-107123DOI: 10.1002/rsa.20469ISI: 000333236500003OAI: oai:DiVA.org:liu-107123DiVA: diva2:722014
#####

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#####

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2014-06-05 Created: 2014-06-05 Last updated: 2014-12-03

Let G = G(n) be a graph on n vertices with maximum degree bounded by some absolute constant Delta. Assign to each vertex v of G a list L(v) of colors by choosing each list uniformly at random from all k-subsets of a color set C of size sigma(n). Such a list assignment is called a random (k,C)-list assignment. In this paper, we are interested in determining the asymptotic probability (as n -greater thaninfinity) of the existence of a proper coloring phi of G, such that phi(v)is an element of L(v) for every vertex v of G. We show, for all fixed k and growing n, that if sigma(n)=omega(n1/k2), then the probability that G has such a proper coloring tends to 1 as n -greater thaninfinity. A similar result for complete graphs is also obtained: if sigma(n)greater than= 1. 223n and L is a random (3,C)-list assignment for the complete graph K-n on n vertices, then the probability that K-n has a proper coloring with colors from the random lists tends to 1 as n -greater than infinity

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1088",{id:"formSmash:lower:j_idt1088",widgetVar:"widget_formSmash_lower_j_idt1088",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1089_j_idt1091",{id:"formSmash:lower:j_idt1089:j_idt1091",widgetVar:"widget_formSmash_lower_j_idt1089_j_idt1091",target:"formSmash:lower:j_idt1089:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});