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Coloring of G²∖G, for Euclidesian graph G

100%

Junosza-Szaniawski K.

Discussiones Mathematicae Graph Theory

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2005

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tom 25

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nr 1-2

219

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Combinatorial lemmas for polyhedrons I

63%

Idzik A., Junosza-Szaniawski K.

Discussiones Mathematicae Graph Theory

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2006

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tom 26

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nr 3

439-338

EN

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.

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Combinatorial lemmas for polyhedrons

63%

Idzik A., Junosza-Szaniawski K.

Discussiones Mathematicae Graph Theory

|

2005

|

tom 25

|

nr 1-2

95-102

EN

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.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

3 Junosza-Szaniawski K.

2 Idzik A.

1 2006

2 2005

Coloring of G²∖G, for Euclidesian graph G

Combinatorial lemmas for polyhedrons I

Combinatorial lemmas for polyhedrons