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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});
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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
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##### 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
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