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Combinatorica

, Volume 37, Issue 5, pp 953–964 | Cite as

On the chromatic number of a simplicial complex

  • Konstantin GolubevEmail author
Original Paper

Abstract

In [3] 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.

Mathematics Subject Classification (2000)

05E45 05A20 05C15 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.The Einstein Institute of MathematicsThe Hebrew University of JerusalemGivat Ram, JerusalemIsrael

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