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The maximum number of complementary facets of a simplicial polytope

✍ Scribed by Walter D. Morris Jr.

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
601 KB
Volume
36
Category
Article
ISSN
0166-218X

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πŸ“œ SIMILAR VOLUMES

Upper Bounds on the Maximal Number of Fa
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✍ TamΓ‘s Fleiner; Volker Kaibel; GΓΌnter Rote πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 157 KB

We prove two new upper bounds on the number of facets that a d-dimensional 0/1-polytope can have. The first one is 2(d -1)!+2(d -1) (which is the best one currently known for small dimensions), while the second one of O((d -2)!) is the best known bound for large dimensions.

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It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It