Lower bounds on the chromatic number of random graphs

@article{Ayre2021LowerBO,
  title={Lower bounds on the chromatic number of random graphs},
  author={Peter J. Ayre and Amin Coja-Oghlan and Catherine S. Greenhill},
  journal={ArXiv},
  year={2021},
  volume={abs/1812.09691}
}
We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborova and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation method from mathematical physics. In the case of random regular graphs the lower bound can be expressed algebraically, while in the case of the binomial random we obtain a variational formula. As an application we calculate improved explicit lower bounds on… 
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