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arXiv · 1207.3761

The Graphs of Planar Soap Bubbles

David Eppstein
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Abstract

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 Moebius transformations, an application of Moebius invariance to prove bridgelessness, and a Moebius-invariant power diagram of circles previously developed by the author for its applications in graph drawing.

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David Eppstein. 2012-07-16. The Graphs of Planar Soap Bubbles. https://arxiv.org/abs/1207.3761

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