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arXiv · 1907.09942

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

A. O. Ivanov·A. A. Tuzhilin
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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 $G$.

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BibTeXRIS

A. O. Ivanov, A. A. Tuzhilin. 2019-07-22. The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces. https://arxiv.org/abs/1907.09942

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