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0-Efficient Triangulations of 3-Manifolds
efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulationExpand
Compression Theorems and Steiner Ratios on Spheres
TLDR
Using the compression theorem, the Steiner ratio on spheres is proved to be the same as on the Euclidean plane, namely $$backslash \bar 3/2$$ . Expand
The Steiner ratio conjecture for six points
TLDR
One proves the Steiner ratio conjecture for six points by using a variational approach to find a shortest network S in the plane R 2 connecting a given set X of n points. Expand
Algorithms for essential surfaces in 3-manifolds
In this paper we outline several algorithms to find essential surfaces in 3dimensional manifolds. In particular, the classical decomposition theorems of 3-manifolds ( Kneser-Milnor connected sumExpand
PL equivariant surgery and invariant decompositions of 3-manifolds
Using normal surface theory [H,, J2], we introduce the notion of least weight normal surfaces. The weight of a normal surface is a nonnegative integer invariant of the normal isotopy class of theExpand
Degree-five Steiner points cannot reduce network costs for planar sets
TLDR
It is shown that a degree-five Steiner point can never appear in a least-cost planar network; that is, it is actedally increased in the cost of the network. Expand
Minimal Steiner Trees for 2k×2k Square Lattices
TLDR
This paper proves a conjecture that the minimal Steiner trees for the set of points comprising the vertices of a 2k×2ksquare lattice are given by Chung, Graham, and Gardner. Expand
Even triangulations of n–dimensional pseudo-manifolds
This paper introduces even triangulations of n-dimensional pseudo-manifolds and links their combinatorics to the topology of the pseudo-manifolds. This is done via normal hypersurface theory and theExpand
Minimal triangulations for an infinite family of lens spaces
The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein in earlier work, and, unless the lens space is L(3,1), a layered triangulation with the minimal number ofExpand
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