Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Volume 3122 of the series Lecture Notes in Computer Science pp 219-228

The Chromatic Number of Random Regular Graphs

  • Dimitris AchlioptasAffiliated withMicrosoft Research
  • , Cristopher MooreAffiliated withUniversity of New Mexico

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Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k+1, or k+2.