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ArticleOriginal scientific text

Title

Combinatorial lemmas for polyhedrons I

Authors 1, 2, 3

Affiliations

  1. Akademia Świętokrzyska, Świętokrzyska 15, 25-406 Kielce, Poland
  2. Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warsaw, Poland
  3. Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Abstract

We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also derived.

Keywords

ENG
b-balanced simplex, labelling, polyhedron, simplicial complex, Sperner lemma

Bibliography

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Discussiones Mathematicae Graph Theory
2006/26/3
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Pages:
439-338
Main language of publication
English
Received
2005-12-02
Accepted
2006-10-03
Published
2006

DOI: 10.7151/dmgt.1336

Exact and natural sciences