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Distinguishing Classes of Intersection Graphs of Homothets or Similarities of Two Convex Disks

Authors Mikkel Abrahamsen , Bartosz Walczak

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Author Details

Mikkel Abrahamsen
  • BARC, University of Copenhagen, Denmark
Bartosz Walczak
  • Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

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Mikkel Abrahamsen and Bartosz Walczak. Distinguishing Classes of Intersection Graphs of Homothets or Similarities of Two Convex Disks. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 2:1-2:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • geometric intersection graph
  • convex disk
  • homothet
  • similarity


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