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Metric Graph Approximations of Geodesic Spaces
Published 14 Sep 2018 in math.MG | (1809.05566v5)
Abstract: We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitable multiplicative constant, Reeb graphs of distance functions to a point provide optimal approximation in the Gromov-Hausdsorff sense.
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