The minimum semidefinite rank of the complement of partial \(k\)-trees

DOI10.1016/j.laa.2010.11.013zbMath1213.05173OpenAlexW2029574412MaRDI QIDQ627949

Hein van der Holst, John Sinkovic

Publication date: 4 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.11.013

zbMATH Keywords

minimum rankgraph complementorthogonal representationpartial \(k\)-trees

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (7)

On the graph complement conjecture for minimum rank ⋮ Sphere representations, stacked polytopes, and the Colin de Verdière number of a graph ⋮ The inverse inertia problem for the complements of partial \(k\)-trees ⋮ Unnamed Item ⋮ Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization ⋮ On the graph complement conjecture for minimum semidefinite rank ⋮ Graph complement conjecture for classes of shadow graphs

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• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
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• A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs

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