conference paper published yes Henry Adams author Sushovan Majhi author Fedor Manin author Ziga Virk author 2E36B656-F248-11E8-B48F-1D18A9856A87 Nicolò Zava author c8b3499c-7a77-11eb-b046-aa368cbbf2ad0000-0001-8686-1888 HeEd department SoCG: Symposium on Computational Geometry Algebraic Footprints of Geometric Features in Homology project Let G be a finite, connected metric graph and let X be a subset of G. If X is sufficiently dense in G, we show that the Gromov-Hausdorff distance matches the Hausdorff distance, namely d_GH(G,X) = d_H(G,X). When the metric graph is the circle G = S¹ with circumference 2π, a recent study established the equality d_GH(S¹,X) = d_H(S¹,X) whenever d_GH(S¹,X) < π/6. Our results relax this hypothesis to d_GH(S¹,X) < π/3, and furthermore, we show that the constant π/3 is the best possible. We lower bound the Gromov-Hausdorff distance d_GH(G,X) by the Hausdorff distance d_H(G,X) via a simple topological obstruction: the existence of a possibly discontinuous function f: G → X with too small distortion contradicts the connectedness of G. https://research-explorer.ista.ac.at/download/22003/22115/2026_LIPIcSSoCG_Adams.pdf application/pdfno Schloss Dagstuhl - Leibniz-Zentrum für Informatik2026New Brunswick, NJ, United States eng Gromov–Hausdorff distancedistortionconnectednessBorsuk–Ulam theorem 1868-8969 9783959774185 2411.0918210.4230/LIPIcs.SoCG.2026.3 367 H. Adams, S. Majhi, F. Manin, Z. Virk, N. Zava, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. Adams, H., Majhi, S., Manin, F., Virk, Z., &#38; Zava, N. (2026). Lower bounding the Gromov–Hausdorff distance in metric graphs. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">https://doi.org/10.4230/LIPIcs.SoCG.2026.3</a> Adams, Henry, Sushovan Majhi, Fedor Manin, Ziga Virk, and Nicolò Zava. “Lower Bounding the Gromov–Hausdorff Distance in Metric Graphs.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">https://doi.org/10.4230/LIPIcs.SoCG.2026.3</a>. Adams H, Majhi S, Manin F, Virk Z, Zava N. Lower bounding the Gromov–Hausdorff distance in metric graphs. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">10.4230/LIPIcs.SoCG.2026.3</a> Adams, Henry, et al. “Lower Bounding the Gromov–Hausdorff Distance in Metric Graphs.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 3:1-3:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">10.4230/LIPIcs.SoCG.2026.3</a>. H. Adams, S. Majhi, F. Manin, Z. Virk, and N. Zava, “Lower bounding the Gromov–Hausdorff distance in metric graphs,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367. Adams H, Majhi S, Manin F, Virk Z, Zava N. 2026. Lower bounding the Gromov–Hausdorff distance in metric graphs. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 3:1-3:16. 220032026-06-14T22:01:44Z2026-06-22T08:49:17Z