The Chromatic Number of Random Graphs for Most Average Degrees

Amin Coja-Oghlan, Dan Vilenchik

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

For a fixed number d >0 and n large, let G(n,d/n) be the random graph on n vertices in which any two vertices are connected with probability d/n independently. The problem of determining the chromatic number of G(n,d/n) goes back to the famous 1960 article of Erdös and Rényi that started the theory of random graphs [Magayar Tud. Akad. Mat. Kutato Int. Kozl. 5 (1960) 17-61]. Progress culminated in the landmark paper of Achlioptas and Naor [Ann. Math. 162 (2005) 1333-1349], in which they calculate the chromatic number precisely for all d in a set S⊂(0,∞) of asymptotic density limz→∞ 10z= 1S = 1/2 , and up to an additive error of one for the remaining d. Here we obtain a near-complete answer by determining the chromatic number of G(n,d/n) for all din a set of asymptotic density 1.

Original languageEnglish
Pages (from-to)5801-5859
Number of pages59
JournalInternational Mathematics Research Notices
Volume2016
Issue number19
DOIs
StatePublished - 1 Jan 2016

ASJC Scopus subject areas

  • General Mathematics

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