Spectral Bounds on the Chromatic Number
نویسنده
چکیده
The purpose of this paper is to discuss spectral bounds on the chromatic number of a graph. The classic result by Hoffman, where λ1 and λn are respectively the maximum and minimum eigenvalues of the adjacency matrix of a graph G, is χ(G) ≥ 1− λ1 λn . It is possible to discuss the coloring of Hermitian matrices in general. Nikiforov developed a spectral bound on the chromatic number of such matrices, which enables the formulation of a chromatic bound based on eigenvalues of tweaked adjacency matrices specifically the normalized Laplacian.
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