Abstract:For smooth convex disks $A$, i.e., convex compact subsets of the plane with non-empty interior and with at most one tangent at every boundary point, we classify the classes $G^{\text{hom}}(A)$ and $G^{\text{sim}}(A)$ of intersection graphs that can be obtained from homothets and similarities of $A$, respectively. Namely, we prove that $G^{\text{hom}}(A)=G^{\text{hom}}(B)$ if and only if $A$ and $B$ are affine equivalent, and $G^{\text{sim}}(A)=G^{\text{sim}}(B)$ if and only if $A$ and $B$ are similar.
From: Bartosz Walczak [view email]
[v1]
Tue, 10 Aug 2021 11:06:07 UTC (531 KB)
[v2]
Sat, 29 Aug 2026 09:16:10 UTC (334 KB)
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