Multiplicities of eigenvalues and tree-width of graphs

From MaRDI portal
Publication:1569029

DOI10.1006/jctb.1998.1834zbMath1027.05064OpenAlexW2038713190MaRDI QIDQ1569029

Yves Colin de Verdière

Publication date: 25 June 2000

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5ded568897ef1e2943e68d91e7745596025ca98b




Related Items

Throttling for Zero Forcing and VariantsGeneralizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graphThe rotational dimension of a graphUsing a new zero forcing process to guarantee the strong Arnold propertySymplectic geometry, minors and graph LaplaciansThe inertia set of a signed graphVarious characterizations of throttling numbersForbidden minors for the class of graphs \(G\) with \(\xi (G) \leqslant 2\)Some recent progress and applications in graph minor theoryAchievable sets, brambles, and sparse treewidth obstructionsOptimizing Colin de Verdière matrices of \(K_{4,4}\)Signed graphs whose signed Colin de Verdière parameter is twoGraph Searching in a Crime WaveThe mixed search game against an agile and visible fugitive is monotoneVertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graphOn the graph complement conjecture for minimum rankComputing inertia sets using atomsThe minimum semidefinite rank of the complement of partial \(k\)-treesLinkless and flat embeddings in 3-spaceOn the Colin de Verdière number of graphsThe minimum semidefinite rank of a triangle-free graphSome connectivity properties for excluded minors of the graph invariant \(\nu(G)\)Graphs whose positive semi-definite matrices have nullity at most twoParameters Tied to TreewidthUnnamed ItemEssential self-adjointness for combinatorial Schrödinger operators. III: Magnetic fieldsPositive semidefinite matrix completion, universal rigidity and the strong Arnold propertyThree-connected graphs whose maximum nullity is at most threeParameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a GraphA new graph parameter related to bounded rank positive semidefinite matrix completionsExpected values of parameters associated with the minimum rank of a graphOn the graph complement conjecture for minimum semidefinite rankZero forcing parameters and minimum rank problemsThe minimum rank of symmetric matrices described by a graph: a surveyForbidden minor characterizations for low-rank optimal solutions to semidefinite programs over the elliptopeDiscrete holomorphic geometry I. Darboux transformations and spectral curvesUnnamed ItemFresnel integrals and determinantsComplexity of the Positive Semidefinite Matrix Completion Problem with a Rank ConstraintGraphs with magnetic Schrödinger operators of low corankGraph complement conjecture for classes of shadow graphs



Cites Work