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arxiv: 1906.10574 · v1 · pith:NFOYKRTQnew · submitted 2019-06-25 · 🧮 math.MG · math.FA

Solution to Generalized Borsuk Problem in Terms of the Gromov-Hausdorff Distances to Simplexes

Alexander Ivanov , Alexei Tuzhilin This is my paper
classification 🧮 math.MG math.FA
keywords borsukdiameterdistancesgeneralizedgivengromov-hausdorffmetricproblem
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In the present paper the following Generalized Borsuk Problem is studied: Can a given bounded metric space $X$ be partitioned into a given number $m$ (probably an infinite one) of subsets, each of which has a smaller diameter than $X$? We give a complete answer to this question in terms of the Gromov-Hausdorff distance from $X$ to a simplex of cardinality $m$ and having a diameter less than $X$. Here a simplex is a metric space, all whose non-zero distances are the same.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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

    math.MG 2019-07 unverdicted novelty 7.0

    Exact Gromov-Hausdorff distances are derived between arbitrary simplexes and 2-distance spaces, yielding a complete solution to the generalized Borsuk problem and expressions for graph clique cover and chromatic numbers.

  2. The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces

    math.MG 2019-07 unverdicted novelty 5.0

    New closed-form expression for Gromov-Hausdorff distance between a simplex and a bounded metric space (under cardinality condition), extended to exact distance with ultrametric spaces.