Eigenvalues and colorings of digraphs

DOI10.1016/j.laa.2009.05.027zbMath1218.05097OpenAlexW2091452762MaRDI QIDQ962116

Bojan Mohar

Publication date: 6 April 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.05.027

zbMATH Keywords

eigenvaluedigraphspectral radiuschromatic numbernon-negative matrixdigraph coloringacyclic setbrooks theorem

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Coloring of graphs and hypergraphs (05C15) Directed graphs (digraphs), tournaments (05C20)

Related Items (24)

The \(m\)-degenerate chromatic number of a digraph ⋮ Digraphs and Variable Degeneracy ⋮ Dichromatic polynomial of product digraphs ⋮ The minimum number of edges in 4-critical digraphs of given order ⋮ Sharp bounds for Laplacian spectral moments of digraphs with a fixed dichromatic number ⋮ Four proofs of the directed Brooks' theorem ⋮ Various bounds on the minimum number of arcs in a \(k\)-dicritical digraph ⋮ The \(A_\alpha\) spectral moments of digraphs with a given dichromatic number ⋮ Two results on the digraph chromatic number ⋮ Geometric and spectral analysis on weighted digraphs ⋮ New eigenvalue bound for the fractional chromatic number ⋮ Spectral radius of digraphs with given dichromatic number ⋮ The distance spectral radius of digraphs ⋮ Large regular bipartite graphs with median eigenvalue 1 ⋮ Colorings and spectral radius of digraphs ⋮ The edge density of critical digraphs ⋮ Spectral radius of strongly connected digraphs ⋮ A note on coloring digraphs of large girth ⋮ Complex adjacency spectra of digraphs ⋮ A Cvetković-type theorem for coloring of digraphs ⋮ Hajós and Ore constructions for digraphs ⋮ Colorings in digraphs from the spectral radius ⋮ A new kind of Hermitian matrices for digraphs ⋮ The signless Laplacian and distance signless Laplacian spectral radius of digraphs with some given parameters

Cites Work

• Spectra of digraphs
• The dichromatic number of a digraph
• Matrix Analysis
• Circular colorings of edge-weighted graphs
• The circular chromatic number of a digraph
• The Eigenvalues of a Graph and Its Chromatic Number
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