Combinatorial lemmas for polyhedrons I
Adam Idzik ; Konstanty Junosza-Szaniawski
Discussiones Mathematicae Graph Theory, Tome 26 (2006), p. 439-338 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:270349 
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Adam Idzik; Konstanty Junosza-Szaniawski. Combinatorial lemmas for polyhedrons I. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 439-338. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1336/

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