The concentration of the chromatic number of random graphs

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Abstract

We prove that for every constant δ > 0 the chromatic number of the random graph G(n,p) with p = n-1/2-δ is asymptotically almost surely concentrated in two consecutive values. This implies that for any β < 1/2 and any integer valued function r(n)≤O(nβ) there exists a function p(n) such that the chromatic number of G(n,p(n)) is precisely r(n) asymptotically almost surely.

Original languageEnglish
Pages (from-to)303-313
Number of pages11
JournalCombinatorica
Volume17
Issue number3
DOIs
StatePublished - 1997

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