License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.2
URN: urn:nbn:de:0030-drops-178523
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17852/
Abrahamsen, Mikkel ;
Walczak, Bartosz
Distinguishing Classes of Intersection Graphs of Homothets or Similarities of Two Convex Disks
Abstract
For smooth convex disks A, i.e., convex compact subsets of the plane with non-empty interior, we classify the classes G^{hom}(A) and G^{sim}(A) of intersection graphs that can be obtained from homothets and similarities of A, respectively. Namely, we prove that G^{hom}(A) = G^{hom}(B) if and only if A and B are affine equivalent, and G^{sim}(A) = G^{sim}(B) if and only if A and B are similar.
BibTeX - Entry
@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2023.2,
author = {Abrahamsen, Mikkel and Walczak, Bartosz},
title = {{Distinguishing Classes of Intersection Graphs of Homothets or Similarities of Two Convex Disks}},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
pages = {2:1--2:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-273-0},
ISSN = {1868-8969},
year = {2023},
volume = {258},
editor = {Chambers, Erin W. and Gudmundsson, Joachim},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17852},
URN = {urn:nbn:de:0030-drops-178523},
doi = {10.4230/LIPIcs.SoCG.2023.2},
annote = {Keywords: geometric intersection graph, convex disk, homothet, similarity}
}
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Keywords: |
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geometric intersection graph, convex disk, homothet, similarity |
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Collection: |
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39th International Symposium on Computational Geometry (SoCG 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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09.06.2023 |
