Sharp concentration of the equitable chromatic number of dense random graphs

@article{Heckel2019SharpCO,
  title={Sharp concentration of the equitable chromatic number of dense random graphs},
  author={A. Heckel},
  journal={Combinatorics, Probability and Computing},
  year={2019},
  volume={29},
  pages={213 - 233}
}
  • A. Heckel
  • Published 20 December 2017
  • Mathematics, Computer Science
  • Combinatorics, Probability and Computing
Abstract An equitable colouring of a graph G is a vertex colouring where no two adjacent vertices are coloured the same and, additionally, the colour class sizes differ by at most 1. The equitable chromatic number χ=(G) is the minimum number of colours required for this. We study the equitable chromatic number of the dense random graph ${\mathcal{G}(n,m)}$ where $m = \left\lfloor {p\left( \matrix{ n \cr 2 \cr} \right)} \right\rfloor $ and 0 < p < 0.86 is constant. It is a well-known question… 
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