New Spectral Bounds on the Chromatic Number Encompassing all Eigenvalues of the Adjacency Matrix
نویسندگان
چکیده
منابع مشابه
New Spectral Bounds on the Chromatic Number Encompassing all Eigenvalues of the Adjacency Matrix
The purpose of this article is to improve existing lower bounds on the chromatic number χ. Let μ1, . . . , μn be the eigenvalues of the adjacency matrix sorted in non-increasing order. First, we prove the lower bound χ > 1 + maxm{ ∑m i=1 μi/ − ∑m i=1 μn−i+1} for m = 1, . . . , n − 1. This generalizes the Hoffman lower bound which only involves the maximum and minimum eigenvalues, i.e., the case...
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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 matr...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2735