Gromov–Hausdorff distances to simplexes and some applications to discrete optimisation

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.