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.[more]
Non-planar quartic graphs have geometric thickness 2 , and therefore have thickness 2.[less]
 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.
 D. Eppstein. "The Geometry Junkyard: Layered Graph Drawing." (Sep 18, 2015) www.ics.uci.edu/~eppstein/junkyard/thickness.
 Wikipedia. "Thickness (Graph Theory)." (Sep 18, 2015) en.wikipedia.org/wiki/Thickness_(graph_theory).
Wolfram Demonstrations Project
Published: September 21 2015