A characterization of simplicial polytopes with \(g_{2}=1\)

DOI10.1016/j.jcta.2009.12.011zbMath1209.52007arXiv0804.1813OpenAlexW2099581288MaRDI QIDQ618296

Eyal Novinsky, Eran Nevo

Publication date: 14 January 2011

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

Full work available at URL: https://arxiv.org/abs/0804.1813

zbMATH Keywords

polytopehomology spheregraph rigidity

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Planar graphs; geometric and topological aspects of graph theory (05C10)

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Cites Work

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• Rigidity and the lower bound theorem. I
• A characterization of simplicial polytopes with \(g_{2}=1\)
• Minimal triangulations of sphere bundles over the circle
• Topological finiteness for edge-vertex enumeration
• Many triangulated spheres
• The number of faces of a simplicial convex polytope
• The rigidity of graphs. II
• A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
• Manifolds with few vertices
• Domination numbers and homology
• Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
• Skeletal rigidity of simplicial complexes. II
• The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold
• Graph theorems for manifolds
• The minimum number of vertices of a simple polytope
• Spheres with few vertices
• A proof of the lower bound conjecture for convex polytopes
• Higher minors and van Kampen's obstruction
• Partial Differential Relations
• The Rigidity of Graphs
• Lectures on Polytopes