Colouring the normalized Laplacian
Combinatorics
2019-10-16 v1
Abstract
We apply Cauchy's interlacing theorem to derive some eigenvalue bounds to the chromatic number using the normalized Laplacian matrix, including a combinatorial characterization of when equality occurs. Further, we introduce some new expansion type of parameters which generalize the Cheeger constant of a graph, and relate them to the colourings which meet our eigenvalue bound with equality. Finally, we exhibit a family of examples, which include the graphs that appear in the statement of the Erd\H{o}s-Faber-Lov\'asz conjecture.
Cite
@article{arxiv.1910.06947,
title = {Colouring the normalized Laplacian},
author = {Gabriel Coutinho and Rafael Grandsire and Célio Passos},
journal= {arXiv preprint arXiv:1910.06947},
year = {2019}
}
Comments
A version of this paper is published on the proceedings of LAGOS 2019