Distinguishing classes of intersection graphs of homothets or similarities of two convex disks

08/10/2021

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by   Mikkel Abrahamsen, et al.

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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.