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