Sets admitting connection by graphs of finite length
Alexander Ivanov, Igor Mikhailovich Nikonov, Alexey Avgustinovich Tuzhilin · Sbornik Mathematics · 2005
The aim of this paper is the description and study of the properties of the subsets of a metric space? that can be connected by a graph of finite length. We obtain a criterion describing these sets, find several geometric properties of them (in the case ), and derive a formula for calculating the length of a minimal spanning tree on as the integral of a certain function constructed by?.