The graphs of planar soap bubbles

Authors:
David Eppstein
Affiliations:
University of California, Irvine, Irvine, CA, USA
Venue:
Proceedings of the twenty-ninth annual symposium on Computational geometry
Year:
2013

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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 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.