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arXiv · 1910.06947

Colouring the normalized Laplacian

Gabriel Coutinho·Rafael Grandsire·Célio Passos
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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 Erdős-Faber-Lovász conjecture.

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Gabriel Coutinho, Rafael Grandsire, Célio Passos. 2019-10-15. Colouring the normalized Laplacian. https://doi.org/10.1016/j.entcs.2019.08.031

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