Guaranteeing Hausdorff-Gromov-Hausdorff Equality for Metric Graphs

2026/07/29 by Paul Schott
Mathematics · #math.MG

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arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We prove the equality of Hausdorff and Gromov-Hausdorff distance d_GH(G, U) = d_H(G, U) for a metric graph G and a subset U ⊆ G, given that the Hausdorff distance between G and U is attained not just near the leaves of G and the Gromov-Hausdorff distance is not too big compared to the graph's systole.

Citations

• Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
• Computational Aspects of the Gromov–Hausdorff Distance and its Application in Non-rigid Shape Matching
• Computing the Gromov-Hausdorff Distance for Metric Trees

Related

• Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
• The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces
• Gromov-Hausdorff distances between quotient metric spaces
• Computing the Gromov-Hausdorff Distance for Metric Trees
• Calculating Gromov-Hausdorff distance by means of asymptotic dimension