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Mathematics > Combinatorics

arXiv:1812.08640 (math)
[Submitted on 20 Dec 2018 (v1), last revised 11 Feb 2020 (this version, v3)]

Title:Vertex-Facet Assignments For Polytopes

Authors:Thomas Jahn, Martin Winter
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Abstract:Motivated by the search for reduced polytopes, we consider the following question: For which polytopes exists a vertex-facet assignment, that is, a matching between vertices and non-incident facets, so that the matching covers either all vertices, or all facets? We provide general conditions for the existence of such an assignment. We conclude that such exist for all simple and simplicial polytopes, as well as all polytopes of dimension $d\le 6$. We construct counterexample in all dimensions $d\ge 7$.
Comments: Beitr Algebra Geom (2020)
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
MSC classes: 05D15, 52B05
Cite as: arXiv:1812.08640 [math.CO]
  (or arXiv:1812.08640v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1812.08640
Related DOI: https://doi.org/10.1007/s13366-020-00504-9

Submission history

From: Martin Winter [view email]
[v1] Thu, 20 Dec 2018 15:38:24 UTC (54 KB)
[v2] Fri, 3 May 2019 13:56:48 UTC (75 KB)
[v3] Tue, 11 Feb 2020 15:12:02 UTC (79 KB)
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