On the graph complement conjecture for minimum semidefinite rank

DOI10.1016/j.laa.2011.03.011zbMath1221.05240OpenAlexW2063369945WikidataQ123014379 ScholiaQ123014379MaRDI QIDQ551287

Lon H. Mitchell

Publication date: 15 July 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.2011.03.011

zbMATH Keywords

minimum semidefinite ranktree-widthstrong Arnold hypothesis

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 (5)

Unnamed Item ⋮ Sphere representations, stacked polytopes, and the Colin de Verdière number of a graph ⋮ Positive semidefinite zero forcing ⋮ Bounds on minimum semidefinite rank of graphs ⋮ Graph complement conjecture for classes of shadow graphs

Cites Work

• Unnamed Item
• On the graph complement conjecture for minimum rank
• The minimum semidefinite rank of the complement of partial \(k\)-trees
• Linearly independent vertices and minimum semidefinite rank
• Zero forcing parameters and minimum rank problems
• The minimum rank of symmetric matrices described by a graph: a survey
• More on extremal positive semidefinite doubly stochastic matrices
• A partial k-arboretum of graphs with bounded treewidth
• Multiplicities of eigenvalues and tree-width of graphs
• Extreme chordal doubly nonnegative matrices with given row sums
• On Complementary Graphs
• Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph

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