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ArticleOriginal scientific text

Title

Combinatorial lemmas for polyhedrons

Authors 1, 2, 3

Affiliations

  1. Akademia Świetokrzyska, 15 Świetokrzyska street, 25-406 Kielce, Poland
  2. Institute of Computer Science, Polish Academy of Sciences, 21 Ordona street, 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 to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a polyhedron to be an onto function.

Keywords

ENG
KKM covering, labelling, primoid, pseudomanifold, simplicial complex, Sperner lemma

Bibliography

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Discussiones Mathematicae Graph Theory
2005/25/1-2
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Pages:
95-102
Main language of publication
English
Published
2005

DOI: 10.7151/dmgt.1264

Exact and natural sciences