Another paper in Aequationes Mathematicae

An analogue of a theorem of Steinitz for ball polyhedra in R-3
Sami Mezal Almohammad, Zsolt Lángi, Márton Naszódi

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 ℝ3.