The graphs of planar soap bubbles
David Eppstein · 2013
We characterize the graphs formed by two-dimensional soap bubbles as being exactly the 3-regular bridgeless planar multigraphs. Our characterization combines a local characterization of soap bubble graphs in terms of the curvatures of arcs meeting at common vertices, a proof that this characterization remains invariant under Mobius transformations, an application of Mobius invariance to prove bridgelessness, and a Mobius-invariant power diagram of circles previously developed by the author for applications in graph drawing.