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- Balinski's_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.".
- Balinski's_theorem wikiPageID "24732291".
- Balinski's_theorem wikiPageRevisionID "583638311".
- Balinski's_theorem hasPhotoCollection Balinski's_theorem.
- Balinski's_theorem subject Category:Graph_connectivity.
- Balinski's_theorem subject Category:Polyhedral_combinatorics.
- Balinski's_theorem subject Category:Theorems_in_discrete_geometry.
- Balinski's_theorem subject Category:Theorems_in_graph_theory.
- Balinski's_theorem type Abstraction100002137.
- Balinski's_theorem type Communication100033020.
- Balinski's_theorem type Message106598915.
- Balinski's_theorem type Proposition106750804.
- Balinski's_theorem type Statement106722453.
- Balinski's_theorem type Theorem106752293.
- Balinski's_theorem type TheoremsInCombinatorics.
- Balinski's_theorem type TheoremsInDiscreteMathematics.
- Balinski's_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.".
- Balinski's_theorem label "Balinski's theorem".
- Balinski's_theorem label "バリンスキーの定理".
- Balinski's_theorem sameAs バリンスキーの定理.
- Balinski's_theorem sameAs m.080mywc.
- Balinski's_theorem sameAs Q32182.
- Balinski's_theorem sameAs Q32182.
- Balinski's_theorem sameAs Balinski's_theorem.
- Balinski's_theorem wasDerivedFrom Balinski's_theorem?oldid=583638311.
- Balinski's_theorem isPrimaryTopicOf Balinski's_theorem.