---
OA_place: publisher
OA_type: gold
_id: '22003'
abstract:
- lang: eng
  text: '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.'
acknowledgement: "Funding Henry Adams: Simons Foundation Travel Support for Mathematicians.\r\nŽiga
  Virk: Slovene research agency grant P1-0292.\r\nNicolò Zava: FWF Grant, Project
  number I4245-N35.\r\n"
alternative_title:
- LIPIcs
article_number: 3:1-3:16
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Henry
  full_name: Adams, Henry
  last_name: Adams
- first_name: Sushovan
  full_name: Majhi, Sushovan
  last_name: Majhi
- first_name: Fedor
  full_name: Manin, Fedor
  last_name: Manin
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
- first_name: Nicolò
  full_name: Zava, Nicolò
  id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
  last_name: Zava
  orcid: 0000-0001-8686-1888
citation:
  ama: '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>'
  apa: '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>'
  chicago: 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>.
  ieee: 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.
  ista: '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.'
  mla: 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>.
  short: H. Adams, S. Majhi, F. Manin, Z. Virk, N. Zava, in:, 42nd International Symposium
    on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
    2026.
conference:
  end_date: 2026-06-05
  location: New Brunswick, NJ, United States
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2026-06-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-06-14T22:01:44Z
date_published: 2026-05-27T00:00:00Z
date_updated: 2026-06-22T08:49:17Z
day: '27'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2026.3
external_id:
  arxiv:
  - '2411.09182'
file:
- access_level: open_access
  checksum: 25d27c016409563196b8aecfe5bfdf41
  content_type: application/pdf
  creator: dernst
  date_created: 2026-06-22T08:43:47Z
  date_updated: 2026-06-22T08:43:47Z
  file_id: '22115'
  file_name: 2026_LIPIcSSoCG_Adams.pdf
  file_size: 1091310
  relation: main_file
  success: 1
file_date_updated: 2026-06-22T08:43:47Z
has_accepted_license: '1'
intvolume: '       367'
keyword:
- Gromov–Hausdorff distance
- distortion
- connectedness
- Borsuk–Ulam theorem
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: 42nd International Symposium on Computational Geometry
publication_identifier:
  eissn:
  - 1868-8969
  isbn:
  - '9783959774185'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounding the Gromov–Hausdorff distance in metric graphs
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2026'
...