## Abstract

For a fixed number d >0 and n large, let G(n,d/n) be the random graph on n vertices in which any two vertices are connected with probability d/n independently. The problem of determining the chromatic number of G(n,d/n) goes back to the famous 1960 article of Erdös and Rényi that started the theory of random graphs [Magayar Tud. Akad. Mat. Kutato Int. Kozl. 5 (1960) 17-61]. Progress culminated in the landmark paper of Achlioptas and Naor [Ann. Math. 162 (2005) 1333-1349], in which they calculate the chromatic number precisely for all d in a set S⊂(0,∞) of asymptotic density lim_{z→∞} 1_{0}^{z}= 1_{S} = 1/2 , and up to an additive error of one for the remaining d. Here we obtain a near-complete answer by determining the chromatic number of G(n,d/n) for all din a set of asymptotic density 1.

Original language | English |
---|---|

Pages (from-to) | 5801-5859 |

Number of pages | 59 |

Journal | International Mathematics Research Notices |

Volume | 2016 |

Issue number | 19 |

DOIs | |

State | Published - 1 Jan 2016 |

## ASJC Scopus subject areas

- General Mathematics