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- Balinskis_theorem abstract "In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes. It states that, if one forms an undirected graph from the vertices and edges of a convex d-dimensional polyhedron or polytope (its skeleton), then the resulting graph is at least d-vertex-connected: the removal of any d − 1 vertices leaves a connected subgraph. For instance, for a three-dimensional polyhedron, even if two of its vertices (together with their incident edges) are removed, for any pair of vertices there will still exist a path of vertices and edges connecting the pair.Balinski's theorem is named after mathematician Michel Balinski, who published its proof in 1961, although the three-dimensional case dates back to the earlier part of the 20th century and the discovery of Steinitz's theorem that the graphs of three-dimensional polyhedra are exactly the three-connected planar graphs.".
- Balinskis_theorem thumbnail Balinski.svg?width=300.
- Balinskis_theorem wikiPageID "24732291".
- Balinskis_theorem wikiPageLength "3629".
- Balinskis_theorem wikiPageOutDegree "16".
- Balinskis_theorem wikiPageRevisionID "680300334".
- Balinskis_theorem wikiPageWikiLink Category:Graph_connectivity.
- Balinskis_theorem wikiPageWikiLink Category:Polyhedral_combinatorics.
- Balinskis_theorem wikiPageWikiLink Category:Theorems_in_discrete_geometry.
- Balinskis_theorem wikiPageWikiLink Category:Theorems_in_graph_theory.
- Balinskis_theorem wikiPageWikiLink Connectivity_(graph_theory).
- Balinskis_theorem wikiPageWikiLink Graph_(mathematics).
- Balinskis_theorem wikiPageWikiLink Graph_theory.
- Balinskis_theorem wikiPageWikiLink Linear_programming.
- Balinskis_theorem wikiPageWikiLink Michel_Balinski.
- Balinskis_theorem wikiPageWikiLink N-skeleton.
- Balinskis_theorem wikiPageWikiLink Polyhedral_combinatorics.
- Balinskis_theorem wikiPageWikiLink Polyhedron.
- Balinskis_theorem wikiPageWikiLink Polytope.
- Balinskis_theorem wikiPageWikiLink Simplex_algorithm.
- Balinskis_theorem wikiPageWikiLink Simplex_method.
- Balinskis_theorem wikiPageWikiLink Skeleton_(topology).
- Balinskis_theorem wikiPageWikiLink Steinitzs_theorem.
- Balinskis_theorem wikiPageWikiLink Undirected_graph.
- Balinskis_theorem wikiPageWikiLink File:Balinski.svg.
- Balinskis_theorem wikiPageWikiLinkText "Balinski's theorem".
- Balinskis_theorem hasPhotoCollection Balinskis_theorem.
- Balinskis_theorem wikiPageUsesTemplate Template:Reflist.
- Balinskis_theorem subject Category:Graph_connectivity.
- Balinskis_theorem subject Category:Polyhedral_combinatorics.
- Balinskis_theorem subject Category:Theorems_in_discrete_geometry.
- Balinskis_theorem subject Category:Theorems_in_graph_theory.
- Balinskis_theorem hypernym Statement.
- Balinskis_theorem comment "In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes. It states that, if one forms an undirected graph from the vertices and edges of a convex d-dimensional polyhedron or polytope (its skeleton), then the resulting graph is at least d-vertex-connected: the removal of any d − 1 vertices leaves a connected subgraph.".
- Balinskis_theorem label "Balinski's theorem".
- Balinskis_theorem sameAs バリンスキーの定理.
- Balinskis_theorem sameAs m.080mywc.
- Balinskis_theorem sameAs Q32182.
- Balinskis_theorem sameAs Q32182.
- Balinskis_theorem wasDerivedFrom Balinskis_theoremoldid=680300334.
- Balinskis_theorem depiction Balinski.svg.
- Balinskis_theorem isPrimaryTopicOf Balinskis_theorem.