The Colin de Verdière number and sphere representations of a graph

DOI10.1007/BF01195002zbMath0910.05056MaRDI QIDQ1280274

Andrew Kotlow, László Lovász, Santosh Vempala

Publication date: 14 March 1999

Published in: Combinatorica (Search for Journal in Brave)

zbMATH Keywords

automorphism groupsubdivisionplanar graphsouterplanargraph invariants

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Structural characterization of families of graphs (05C75)

Related Items (24)

Variational analysis of the Ky Fan \(k\)-norm ⋮ The complement problem for linklessly embeddable graphs ⋮ Using a new zero forcing process to guarantee the strong Arnold property ⋮ Apollonian ball packings and stacked polytopes ⋮ Hadwiger numbers of self-complementary graphs ⋮ The Colin de Verdière number and graphs of polytopes ⋮ Spectral operators of matrices ⋮ Constructions stemming from nonseparating planar graphs and their Colin de Verdière invariant ⋮ Plane graphs with straight edges whose bounded faces are acute triangles ⋮ Complete minors in complements of nonseparating planar graphs ⋮ On the graph complement conjecture for minimum rank ⋮ The minimum semidefinite rank of the complement of partial \(k\)-trees ⋮ Sphere representations, stacked polytopes, and the Colin de Verdière number of a graph ⋮ On Euclidean distances and sphere representations ⋮ On the rank of a matrix associated with a graph. ⋮ Boxicity and topological invariants ⋮ The complement of a nIL graph with thirteen vertices is IL ⋮ The extremal function and Colin de Verdière graph parameter ⋮ A note on generic rigidity of graphs in higher dimension ⋮ The Colin de Verdière number and joins of graphs ⋮ Coxeter groups, hyperbolic cubes and acute triangulations ⋮ Spectral Operators of Matrices: Semismoothness and Characterizations of the Generalized Jacobian ⋮ A reduction procedure for the Colin de Verdière number of a graph ⋮ Steinitz representations of polyhedra and the Colin de Verdière number

Cites Work

• Unnamed Item
• On Hadwiger's number---A problem of the Nordhaus-Gaddum type
• Coin graphs, polyhedra, and conformal mapping
• Embeddings of graphs in Euclidean spaces
• Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
• Geometrical embeddings of graphs
• Sachs' linkless embedding conjecture
• A short proof of the planarity characterization of Colin de Verdière
• Infinitesimally Rigid Polyhedra. I. Statics of Frameworks

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