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 triangulation… Expand

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

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 sum… Expand

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 the… Expand

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

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

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 the… Expand

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 of… Expand