The concentration of the chromatic number of random graphs

Noga Alon*, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - 1997


FundersFunder number
USA Israeli BSF
Israel Science Foundation


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