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Facets with fewest vertices

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Abstract

Forv>d≧3, letm(v, d) be the smallest numberm, such that every convexd-polytope withv vertices has a facet with at mostm vertices. In this paper, bounds form(v, d) are found; in particular, for fixedd≧3,

$$\frac{{r - 1}}{r} \leqslant \mathop {\lim \inf }\limits_{\upsilon \to \infty } \frac{{m(\upsilon ,d)}}{\upsilon } \leqslant \mathop {\lim \sup }\limits_{\upsilon \to \infty } \frac{{m(\upsilon ,d)}}{\upsilon } \leqslant \frac{{d - 3}}{{d - 2}}$$

, wherer=[1/3(d+1)].

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References

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Authors and Affiliations

  1. Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364, Budapest V, Hungary

    A. Bezdek & E. Makai Jr.

  2. Department of Geometry, Eötvös Lórand University, Rákóczi ut 5, H-1088, Budapest, Hungary

    K. Bezdek

  3. Department of Mathematics, University College London, Gower Street, WC1E 6BT, GB-London, UK

    P. McMullen

Authors
  1. A. Bezdek
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  2. K. Bezdek
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  3. E. Makai Jr.
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  4. P. McMullen
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Bezdek, A., Bezdek, K., Makai, E. et al. Facets with fewest vertices. Monatshefte für Mathematik 109, 89–96 (1990). https://doi.org/10.1007/BF01302928

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  • DOI: https://doi.org/10.1007/BF01302928

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