On the null space of a Colin de Verdière matrix

DOI10.5802/aif.1703zbMath0923.05038OpenAlexW1589241842MaRDI QIDQ1296155

Alexander Schrijver, László Lovász

Publication date: 12 July 1999

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1999__49_3_1017_0

zbMATH Keywords

planar graphnull spacematriximbeddingouterplanar graphColin de Verdière matrix

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (12)

The strong spectral property for graphs ⋮ Spectral representations of vertex transitive graphs, Archimedean solids and finite Coxeter groups ⋮ Some recent progress and applications in graph minor theory ⋮ Universal completability, least eigenvalue frameworks, and vector colorings ⋮ The Colin de Verdière number and graphs of polytopes ⋮ Linkless and flat embeddings in 3-space ⋮ Eigenpolytope Universality and Graphical Designs ⋮ Nullspace Embeddings for Outerplanar Graphs ⋮ Positive semidefinite matrix completion, universal rigidity and the strong Arnold property ⋮ The strong Arnold property for 4-connected flat graphs ⋮ Steinitz representations of polyhedra and the Colin de Verdière number ⋮ On Vertex Partitions and the Colin de Verdière Parameter

Cites Work

• Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
• On the invariance of Colin de Verdière's graph parameter under clique sums
• A short proof of the planarity characterization of Colin de Verdière
• A Borsuk theorem for antipodal links and a spectral characterization of linklessly embeddable graphs

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