Displaying similar documents to “On hyperbolic 3-manifolds realizing the maximal distance between toroidal Dehn fillings.”

Regulated buildups of 3-configurations

Václav J. Havel (1994)

Archivum Mathematicum

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We deal with two types of buildups of 3-configurations: a generating buildup over a given edge set and a regulated one (according to maximal relative degrees of vertices over a penetrable set of vertices). Then we take account to minimal generating edge sets, i.e., to edge bases. We also deduce the fundamental relation between the numbers of all vertices, of all edges from edge basis and of all terminal elements. The topic is parallel to a certain part of Belousov' “Configurations...

Geometric types of twisted knots

Mohamed Aït-Nouh, Daniel Matignon, Kimihiko Motegi (2006)

Annales mathématiques Blaise Pascal

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Let K be a knot in the 3 -sphere S 3 , and Δ a disk in S 3 meeting K transversely in the interior. For non-triviality we assume that | Δ K | 2 over all isotopies of K in S 3 - Δ . Let K Δ , n ( S 3 ) be a knot obtained from K by n twistings along the disk Δ . If the original knot is unknotted in S 3 , we call K Δ , n a . We describe for which pair ( K , Δ ) and an integer n , the twisted knot K Δ , n is a torus knot, a satellite knot or a hyperbolic knot.

Hypergraphs with large transversal number and with edge sizes at least four

Michael Henning, Christian Löwenstein (2012)

Open Mathematics

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Let H be a hypergraph on n vertices and m edges with all edges of size at least four. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. Lai and Chang [An upper bound for the transversal numbers of 4-uniform hypergraphs, J. Combin. Theory Ser. B, 1990, 50(1), 129–133] proved that τ(H) ≤ 2(n+m)/9, while Chvátal and McDiarmid [Small transversals in hypergraphs, Combinatorica, 1992, 12(1), 19–26] proved that τ(H) ≤ (n + 2m)/6. In this paper, we...