On centrally symmetric graphs
نویسندگان
چکیده
منابع مشابه
Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai’s 3d conjecture for such polytopes (they all have at least 3d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3d + 16 nonempty...
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In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture,A, became known as the “3-conjecture”. It is well-known that the three conjectures hold in dimensions d ≤ 3. We show that in dimension 4 only conjectures A and B are valid, while conjecture C fails. Furthermore, we show that both conje...
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The solutions to axially and centrally symmetric Lamé problems are derived within the displacement, stress and strain-based approach by the specification of the general boundary conditions which encompass all possible combinations of kinematic and kinetic conditions at the inner and outer boundaries. It is shown that the mathematical structure of the governing differential equations in the stra...
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The Hadwiger number H(S) of a topological disk S in R 2 is the maximal number of pairwise nonoverlapping translates of S that touch S. A conjecture of A. Bezdek., K. and W. Kuperberg [2] states that this number is at most eight for any starlike disk. A. Bezdek [1] proved that the Hadwiger number of a starlike disk is at most seventy five. In this note, we prove that the Hadwiger number of any c...
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A centrally symmetric 2d-vertex combinatorial triangulation of the product of spheres S × Sd−2−i is constructed for all pairs of non-negative integers i and d with 0 ≤ i ≤ d − 2. For the case of i = d − 2 − i, the existence of such a triangulation was conjectured by Sparla. The constructed complex admits a vertex-transitive action by a group of order 4d. The crux of this construction is a defin...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 1996
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.1996.125944