Vertex-facet incidences of unbounded polyhedra.
Joswig, Michael, Kaibel, Volker, Pfetsch, Marc E., Ziegler, Günter M. (2001)
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Joswig, Michael, Kaibel, Volker, Pfetsch, Marc E., Ziegler, Günter M. (2001)
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Oleg V. Borodin (1992)
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Lee, Carl W. (2011)
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Bacher, R., Krattenthaler, C. (2011)
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Oleg V. Borodin, Anna O. Ivanova (2017)
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Lebesgue (1940) proved that every 3-polytope P5 of girth 5 has a path of three vertices of degree 3. Madaras (2004) refined this by showing that every P5 has a 3-vertex with two 3-neighbors and the third neighbor of degree at most 4. This description of 3-stars in P5s is tight in the sense that no its parameter can be strengthened due to the dodecahedron combined with the existence of a P5 in which every 3-vertex has a 4-neighbor. We give another tight description of 3-stars in P5s:...
Milica Stojanović (2005)
Matematički Vesnik
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Athanasiadis, Christos A. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Pfeifle, Julian, Ziegler, Günter M. (2004)
Experimental Mathematics
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Adam Idzik, Konstanty Junosza-Szaniawski (2006)
Discussiones Mathematicae Graph Theory
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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...
Datta, Basudeb, Nilakantan, Nandini (2008)
International Journal of Mathematics and Mathematical Sciences
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S. Jendrol, E. Jucovič, M. Trenkler (1989)
Banach Center Publications
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Lawrencenko, Serge, Negami, Seiya, Sabitov, Idjad Kh. (2002)
Beiträge zur Algebra und Geometrie
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