The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces

Abstract

In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called $2$-distance spaces). As a corollary, a complete solution to generalized Borsuk problem for the $2$-distance spaces is obtained. In addition, we derive formulas for the clique covering number and for the chromatic number of an arbitrary graph $G$ in terms of the Gromov-Hausdorff distance between a simplex and an appropriate $2$-distance space constructed by the graph $G$.

10 pages

References in corpus (3)

• Geometry of Compact Metric Space in Terms of Gromov-Hausdorff Distances to Regular Simplexes
• Solution to Generalized Borsuk Problem in Terms of the Gromov-Hausdorff Distances to Simplexes
• The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces

Cited by in corpus (1)

• Polynomial-time algorithms for continuous metrics on atomic clouds of unordered points