An analogue of a theorem of Steinitz for ball polyhedra in $\mathbb{R}^3$

Almohammad, Sami and Lángi, Zsolt and Naszódi, Márton (2020) An analogue of a theorem of Steinitz for ball polyhedra in $\mathbb{R}^3$. AEQUATIONES MATHEMATICAE. ISSN 0001-9054 (In Press)

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Abstract

Steinitz's theorem states that a graph $G$ is the edge-graph of a $3$-dimensional convex polyhedron if and only if, $G$ is simple, plane and $3$-connected. We prove an analogue of this theorem for ball polyhedra, that is, for intersections of finitely many unit balls in $\mathbb{R}^3$.

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