The Graphs of Planar Soap Bubbles
Discrete Mathematics
2012-07-17 v1 Computational Geometry
Metric Geometry
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.
Cite
@article{arxiv.1207.3761,
title = {The Graphs of Planar Soap Bubbles},
author = {David Eppstein},
journal= {arXiv preprint arXiv:1207.3761},
year = {2012}
}
Comments
16 pages, 9 figures