Sharp concentration of the chromatic number on random graphs G n, p

Eli Shamir, Joel Spencer

Research output: Contribution to journalArticle

Abstract

The distribution of the chromatic number on random graphs G n, p is quite sharply concentrated. For fixed p it concentrates almost surely in √n ω(n) consecutive integers where ω(n) approaches infinity arbitrarily slowly. If the average degree pn is less than n 1/6, it concentrates almost surely in five consecutive integers. Large deviation estimates for martingales are used in the proof.

Original languageEnglish (US)
Pages (from-to)121-129
Number of pages9
JournalCombinatorica
Volume7
Issue number1
DOIs
StatePublished - Mar 1987

Fingerprint

Chromatic number
Random Graphs
Consecutive
Integer
Large Deviations
Martingale
Infinity
Estimate

Keywords

  • AMS subject classification (1980): 05C15, 60C05

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)
  • Computational Mathematics

Cite this

Sharp concentration of the chromatic number on random graphs G n, p. / Shamir, Eli; Spencer, Joel.

In: Combinatorica, Vol. 7, No. 1, 03.1987, p. 121-129.

Research output: Contribution to journalArticle

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