Gromov–Hausdorff Distances to Simplexes and Some Applications to Discrete Optimisation

Abstract

Relations between Gromov–Hausdorff distance and Discrete Optimisation problems are
discussed. We use the Gromov–Hausdorff distances to single-distance metric space for solving
the following problems: calculation of lengths of minimum spanning tree edges of a finite metric
space; generalised Borsuk problem; chromatic number and clique cover number of a simple
graph calculation problems.