Coloring complete bipartite graphs from random lists

Michael Krivelevich*, Asaf Nachmias

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Let Kn,n be the complete bipartite graph with n vertices in each side. For each vertex draw uniformly at random a list of size k from a base set S of size s = s(n). In this paper we estimate the asymptotic probability of the existence of a proper coloring from the random lists for all fixed values of k and growing n. We show that this property exhibits a sharp threshold for k ≥ 2 and the location of the threshold is precisely s(n) = 2n for k = 2 and approximately s(n) = n/2k-1ln2 for k ≥ 3.

Original languageEnglish
Pages (from-to)436-449
Number of pages14
JournalRandom Structures and Algorithms
Volume29
Issue number4
DOIs
StatePublished - Dec 2006

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