A proof of Kühnel’s conjecture for \(n\geq k^ 2+3k\). (English) Zbl 0887.52007
The Kühnel’s conjecture for combinatorial 2k-manifolds has been established by W. Kühnel and U. Brehm if the number \(n\) of vertices of M satisfies either \(n \leq 3k + 3\) or \(n \geq k^2 + 4k + 3\). In this paper, the author improves this result by showing that the conjecture is true for \(n \geq k^2 + 3 k\) and so he obtains as a corollary that the statement in the conjecture is true for \(k = 1\) and \(k = 2\).
Reviewer: M.do Rosário Pinto (Porto)
MSC:
| 52B05 | Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) |
| 57Q15 | Triangulating manifolds |
References:
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