Vertex-vectors of quadrangular 3-polytopes with two types of edges
S. Jendrol, E. Jucovič, M. Trenkler (1989)
Banach Center Publications
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Displaying similar documents to “Clique-connecting forest and stable set polytopes”
Vertex-vectors of quadrangular 3-polytopes with two types of edges
All Tight Descriptions of 3-Stars in 3-Polytopes with Girth 5
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:...
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Pfeifle, Julian, Ziegler, Günter M. (2004)
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Athanasiadis, Christos A. (2004)
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Branko Grünbaum, Ernest Jucovič (1974)
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R. Blind, G. Blind (1994)
Discrete & computational geometry
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An extension of Kotzig’s theorem on the minimum weight of edges in -polytopes
Oleg V. Borodin (1992)
Mathematica Slovaca
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On the Weight of Minor Faces in Triangle-Free 3-Polytopes
Oleg V. Borodin, Anna O. Ivanova (2016)
Discussiones Mathematicae Graph Theory
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The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sharp, but it was still unknown whether 21 is sharp. The purpose of this paper is to improve this 21 to 20, which is best possible.