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- Q18394143 subject Q6465283.
- Q18394143 subject Q7007191.
- Q18394143 abstract "In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists a collection of k planar graphs, all having the same set of vertices, such that the union of these planar graphs is G, then the thickness of G is at most k. In other words, the thickness of a graph is the minimal number of planar subgraphs whose union equals to graph G.Thus, a planar graph has thickness 1. Graphs of thickness 2 are called biplanar graphs. The concept of thickness originates in the 1962 conjecture of Frank Harary: For any graph on 9 points, either itself or its complementary graph is non-planar. The problem is equivalent to determining whether the complete graph K9 is biplanar (it is not, and the conjecture is true). A comprehensive survey on the state of the arts of the topic as of 1998 was written by Petra Mutzel, Thomas Odenthal and Mark Scharbrodt.".
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- Q18394143 wikiPageWikiLink Q6465283.
- Q18394143 wikiPageWikiLink Q7007191.
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- Q18394143 wikiPageWikiLink Q913598.
- Q18394143 comment "In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists a collection of k planar graphs, all having the same set of vertices, such that the union of these planar graphs is G, then the thickness of G is at most k. In other words, the thickness of a graph is the minimal number of planar subgraphs whose union equals to graph G.Thus, a planar graph has thickness 1.".
- Q18394143 label "Thickness (graph theory)".