2019/07/22 by Ivanov, A. O., Tuzhilin, A. A.
#51Fxx #52C23 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1907.09942
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.