Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

Cuts and metrics are well-known objects that arise-independently, but with many deep and
fascinating connections-in diverse fields: in graph theory, combinatorial optimization …

The cut method is a powerful tool for the investigation of distance-based (and some other)
molecular structure-descriptors. In this paper a survey on the recent developments of the …

We consider specific additive decompositions d= d 1+…+ dn of metrics, defined on a finite
set X (where a metric may give distance zero to pairs of distinct points). The simplest …

The article surveys structural characterizations of several graph classes defined by distance
properties, which have in part a general algebraic flavor and can be interpreted as subdirect …

If $ G $ is a finite connected graph with vertex set $ V $ and edge set $ E $, a standard way
of defining a distance ${d_G} $ on $ G $ is to define ${d_G}(x, y) $ to be the number of edges …

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently
used principal mathematical and computational tools and techniques of the geometric …

This is the continuation of Part I (this issue). In this second part, we present the following
applications of cut polyhedra: the max-cut problem, the Boole problem and the …

Average distance of a graph is expressed in terms of its canonical metric representation. The
equality can be modified to an inequality in such a way that it characterizes isometric …

Several recent papers have dealt with the problem of obtaining nearly isometric embeddings
of metric spaces into low dimensional L-spaces. Johnson and Schechtman [8], consider …