On the chromatic number of a simplicial complex
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In  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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- A. J. Hoffman: On Eigenvalues and Colorings of Graphs, Graph Theory and its Applications, (ed: B. Harris), Academic Press, (1970), 79–91.Google Scholar