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In the present paper we calculate the Gromov-Hausdorff distance between anarbitrary 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 togeneralized Borsuk problem for the $2$-distance spaces is obtained. Inaddition, we derive formulas for the clique covering number and for thechromatic number of an arbitrary graph $G$ in terms of the Gromov-Hausdorffdistance between a simplex and an appropriate $2$-distance space constructed bythe graph $G$.

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