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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
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
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
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
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