---
res:
  bibo_abstract:
  - '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.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Henry
      foaf_name: Adams, Henry
      foaf_surname: Adams
  - foaf_Person:
      foaf_givenName: Sushovan
      foaf_name: Majhi, Sushovan
      foaf_surname: Majhi
  - foaf_Person:
      foaf_givenName: Fedor
      foaf_name: Manin, Fedor
      foaf_surname: Manin
  - foaf_Person:
      foaf_givenName: Ziga
      foaf_name: Virk, Ziga
      foaf_surname: Virk
      foaf_workInfoHomepage: http://www.librecat.org/personId=2E36B656-F248-11E8-B48F-1D18A9856A87
  - foaf_Person:
      foaf_givenName: Nicolò
      foaf_name: Zava, Nicolò
      foaf_surname: Zava
      foaf_workInfoHomepage: http://www.librecat.org/personId=c8b3499c-7a77-11eb-b046-aa368cbbf2ad
    orcid: 0000-0001-8686-1888
  bibo_doi: 10.4230/LIPIcs.SoCG.2026.3
  bibo_volume: 367
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1868-8969
  - http://id.crossref.org/issn/9783959774185
  dct_language: eng
  dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
  dct_subject:
  - Gromov–Hausdorff distance
  - distortion
  - connectedness
  - Borsuk–Ulam theorem
  dct_title: Lower bounding the Gromov–Hausdorff distance in metric graphs@
...