dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor
Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
dc.contributor.author
Pfeifle, Julián
dc.identifier
Pfeifle, J. Kalai's squeezed three-spheres are polytopal. "Electronic notes in discrete mathematics", 2001, vol. 10, p. 238-241.
dc.identifier
https://hdl.handle.net/2117/7764
dc.description.abstract
In 1988, Kalai [5] extended a construction of Billera and Lee to produce many triangulated(d−1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Goodman and Pollack [2,3], he derived that for every dimension d ≥ 5, most of these(d−1)-spheres are not polytopal. However, for d=4, this reasoning fails. We can now show that, as already conjectured by Kalai, all of his 3-spheres are in fact polytopal. We also give a shorter proof for Hebble and Lee’s result [4] that the dual graphs of these 4-polytopes are Hamiltonian.
dc.description.abstract
Postprint (published version)
dc.format
application/pdf
dc.rights
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights
Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
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Hamiltonian graph theory
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Combinatory logic
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Convex geometry
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Lògica combinatòria
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Geometria convexa
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Hamilton, Sistemes de
dc.title
Kalai's squeezed three-spheres are polytopal
