On the chromatic number of a simplicial complex

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.

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Correspondence to Konstantin Golubev.

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This work is a part of the Ph.D. thesis being written at the Hebrew University of Jerusalem, Israel.

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Golubev, K. On the chromatic number of a simplicial complex. Combinatorica 37, 953–964 (2017). https://doi.org/10.1007/s00493-016-3137-z

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Mathematics Subject Classification (2000)

  • 05E45
  • 05A20
  • 05C15