### 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 language | English (US) |
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Pages (from-to) | 121-129 |

Number of pages | 9 |

Journal | Combinatorica |

Volume | 7 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1987 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Combinatorica*,

*7*(1), 121-129. https://doi.org/10.1007/BF02579208

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

Research output: Contribution to journal › Article

*Combinatorica*, vol. 7, no. 1, pp. 121-129. https://doi.org/10.1007/BF02579208

}

TY - JOUR

T1 - Sharp concentration of the chromatic number on random graphs G n, p

AU - Shamir, Eli

AU - Spencer, Joel

PY - 1987/3

Y1 - 1987/3

N2 - 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.

AB - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=51649150009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649150009&partnerID=8YFLogxK

U2 - 10.1007/BF02579208

DO - 10.1007/BF02579208

M3 - Article

AN - SCOPUS:51649150009

VL - 7

SP - 121

EP - 129

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -