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- Thickness_(graph_theory) 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.".
- Thickness_(graph_theory) wikiPageID "43082178".
- Thickness_(graph_theory) wikiPageLength "7834".
- Thickness_(graph_theory) wikiPageOutDegree "26".
- Thickness_(graph_theory) wikiPageRevisionID "643823888".
- Thickness_(graph_theory) wikiPageWikiLink Approximation_algorithm.
- Thickness_(graph_theory) wikiPageWikiLink Approximation_ratio.
- Thickness_(graph_theory) wikiPageWikiLink Arboricity.
- Thickness_(graph_theory) wikiPageWikiLink Book_embedding.
- Thickness_(graph_theory) wikiPageWikiLink Category:Graph_invariants.
- Thickness_(graph_theory) wikiPageWikiLink Category:Planar_graphs.
- Thickness_(graph_theory) wikiPageWikiLink Circular_layout.
- Thickness_(graph_theory) wikiPageWikiLink Complement_graph.
- Thickness_(graph_theory) wikiPageWikiLink Complementary_graph.
- Thickness_(graph_theory) wikiPageWikiLink Complete_bipartite_graph.
- Thickness_(graph_theory) wikiPageWikiLink Complete_graph.
- Thickness_(graph_theory) wikiPageWikiLink Convex_position.
- Thickness_(graph_theory) wikiPageWikiLink Degeneracy_(graph_theory).
- Thickness_(graph_theory) wikiPageWikiLink Frank_Harary.
- Thickness_(graph_theory) wikiPageWikiLink Glossary_of_graph_theory.
- Thickness_(graph_theory) wikiPageWikiLink Graph_invariant.
- Thickness_(graph_theory) wikiPageWikiLink Graph_property.
- Thickness_(graph_theory) wikiPageWikiLink Graph_theory.
- Thickness_(graph_theory) wikiPageWikiLink Line_segment.
- Thickness_(graph_theory) wikiPageWikiLink NP-complete.
- Thickness_(graph_theory) wikiPageWikiLink NP-completeness.
- Thickness_(graph_theory) wikiPageWikiLink NP-hard.
- Thickness_(graph_theory) wikiPageWikiLink NP-hardness.
- Thickness_(graph_theory) wikiPageWikiLink Petra_Mutzel.
- Thickness_(graph_theory) wikiPageWikiLink Planar_graph.
- Thickness_(graph_theory) wikiPageWikiLink Planar_graphs.
- Thickness_(graph_theory) wikiPageWikiLink Polynomial_time.
- Thickness_(graph_theory) wikiPageWikiLink Simultaneous_embedding.
- Thickness_(graph_theory) wikiPageWikiLink Time_complexity.
- Thickness_(graph_theory) wikiPageWikiLink Tree_(graph_theory).
- Thickness_(graph_theory) wikiPageWikiLink Union_(mathematics).
- Thickness_(graph_theory) wikiPageWikiLink Union_(set_theory).
- Thickness_(graph_theory) wikiPageWikiLinkText "Thickness (graph theory)".
- Thickness_(graph_theory) wikiPageWikiLinkText "thickness".
- Thickness_(graph_theory) hasPhotoCollection Thickness_(graph_theory).
- Thickness_(graph_theory) wikiPageUsesTemplate Template:Math.
- Thickness_(graph_theory) wikiPageUsesTemplate Template:Mvar.
- Thickness_(graph_theory) wikiPageUsesTemplate Template:Reflist.
- Thickness_(graph_theory) subject Category:Graph_invariants.
- Thickness_(graph_theory) subject Category:Planar_graphs.
- Thickness_(graph_theory) hypernym Number.
- Thickness_(graph_theory) 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.".
- Thickness_(graph_theory) label "Thickness (graph theory)".
- Thickness_(graph_theory) sameAs m.010x6_nb.
- Thickness_(graph_theory) sameAs Толщина_графа.
- Thickness_(graph_theory) sameAs Q18394143.
- Thickness_(graph_theory) sameAs Q18394143.
- Thickness_(graph_theory) wasDerivedFrom Thickness_(graph_theory)?oldid=643823888.
- Thickness_(graph_theory) isPrimaryTopicOf Thickness_(graph_theory).