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.
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The generalized Borsuk problem is solved by the criterion that a bounded metric space X admits an m-partition into smaller-diameter sets if and only if its Gromov-Hausdorff distance to an m-point simplex of smaller diameter is positive.
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The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces
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.
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Solution to Generalized Borsuk Problem in Terms of the Gromov-Hausdorff Distances to Simplexes
The generalized Borsuk problem is solved by the criterion that a bounded metric space X admits an m-partition into smaller-diameter sets if and only if its Gromov-Hausdorff distance to an m-point simplex of smaller diameter is positive.