Geodesic
Combinatorial lemmas for polyhedrons
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 95-102.

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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: KKM covering, labelling, primoid, pseudomanifold, simplicial complex, Sperner lemma 
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Idzik, Adam; Junosza-Szaniawski, Konstanty. Combinatorial lemmas for polyhedrons. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 95-102. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a10/

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