Thickness-2 Graphs

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If the edges of a graph can be partitioned into two planar graphs, it has thickness 2 (a biplanar graph). This Demonstration shows some thickness-2 embeddings of various quartic graphs. In the first step a Hamiltonian cycle is chosen. One of the graphs, the icosidodecahedral graph (26), is planar and actually has thickness 1.

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Non-planar quartic graphs have geometric thickness 2 [1], and therefore have thickness 2.

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Contributed by: Ed Pegg Jr (September 2015)
Open content licensed under CC BY-NC-SA


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References

[1] Christian A. Duncan, David Eppstein and Stephen G. Kobourov, "The Geometric Thickness of Low Degree Graphs", 24 Dec 2003. http://arxiv.org/abs/cs/0312056.

[2] D. Eppstein. "The Geometry Junkyard: Layered Graph Drawing." (Sep 18, 2015) www.ics.uci.edu/~eppstein/junkyard/thickness.

[3] Wikipedia. "Thickness (Graph Theory)." (Sep 18, 2015) en.wikipedia.org/wiki/Thickness_(graph_theory).



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