liu.seSearch for publications in DiVA

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt176",{id:"formSmash:upper:j_idt176",widgetVar:"widget_formSmash_upper_j_idt176",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt181_j_idt183",{id:"formSmash:upper:j_idt181:j_idt183",widgetVar:"widget_formSmash_upper_j_idt181_j_idt183",target:"formSmash:upper:j_idt181:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Coloring graphs of various maximum degree 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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2018 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 52, no 1, p. 54-73Article in journal (Refereed) Published
##### Abstract [en]

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

WILEY , 2018. Vol. 52, no 1, p. 54-73
##### Keywords [en]

coloring from random lists; list coloring; random list
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:liu:diva-143607DOI: 10.1002/rsa.20725ISI: 000415879600003OAI: oai:DiVA.org:liu-143607DiVA, id: diva2:1165638
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt534",{id:"formSmash:j_idt534",widgetVar:"widget_formSmash_j_idt534",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt540",{id:"formSmash:j_idt540",widgetVar:"widget_formSmash_j_idt540",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt546",{id:"formSmash:j_idt546",widgetVar:"widget_formSmash_j_idt546",multiple:true});
##### Note

Let G=G(n) be a graph on n vertices with maximum degree = (n). Assign to each vertex v of G a list L(v) of colors by choosing each list independently and uniformly at random from all k-subsets of a color set C of size C sigma=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 ) of the existence of a proper coloring phi of G, such that phi(v)L(v) for every vertex v of G, a so-called L-coloring. We give various lower bounds on sigma, in terms of n, k, and , which ensures that with probability tending to 1 as n there is an L-coloring of G. In particular, we show, for all fixed k and growing n, that if sigma(n)=(n1/k21/k) and =O(n), then the probability that G has an L-coloring tends to 1 as n. If k2 and =(n1/2), then the same conclusion holds provided that sigma=(). We also give related results for other bounds on , when k is constant or a strictly increasing function of n.

Funding Agencies|SVeFUM; Mittag-Leffler Institute

Available from: 2017-12-13 Created: 2017-12-13 Last updated: 2018-01-03
doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1560",{id:"formSmash:j_idt1560",widgetVar:"widget_formSmash_j_idt1560",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1613",{id:"formSmash:lower:j_idt1613",widgetVar:"widget_formSmash_lower_j_idt1613",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1614_j_idt1616",{id:"formSmash:lower:j_idt1614:j_idt1616",widgetVar:"widget_formSmash_lower_j_idt1614_j_idt1616",target:"formSmash:lower:j_idt1614:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});