Random regular graphs of non-constant degree: Concentration of the chromatic number

Sonny Ben-Shimon*, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this work we show that with high probability the chromatic number of a graph sampled from the random regular graph model Gn, d for d = o (n1 / 5) is concentrated in two consecutive values, thus extending a previous result of Achlioptas and Moore. This concentration phenomena is very similar to that of the binomial random graph model G (n, p) with p = frac(d, n). Our proof is largely based on ideas of Alon and Krivelevich who proved this two-point concentration result for G (n, p) for p = n- δ where δ > 1 / 2. The main tool used to derive such a result is a careful analysis of the distribution of edges in Gn, d, relying both on the switching technique and on bounding the probability of exponentially small events in the configuration model.

Original languageEnglish
Pages (from-to)4149-4161
Number of pages13
JournalDiscrete Mathematics
Volume309
Issue number12
DOIs
StatePublished - 28 Jun 2009

Funding

FundersFunder number
USA–Israel BSF
Israel Science Foundation

    Keywords

    • Chromatic number concentration
    • Edge distribution
    • Random regular graphs

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