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arXiv · 1306.4818

On the chromatic number of a simplicial complex

Konstantin Golubev
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Abstract

In [Ho] A.J. Hoffman proved a lower bound on the chromatic number of a graph in the terms of the largest and the smallest eigenvalues of its adjacency matrix. In this paper, we prove a higher dimensional version of this result and give a lower bound on the chromatic number of a pure $d$-dimensional simplicial complex in the terms of the spectra of the higher Laplacian operators.

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Konstantin Golubev. 2015-11-17. On the chromatic number of a simplicial complex. https://doi.org/10.1007/s00493-016-3137-z

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