Balinski's Theorem describes the graph-theoretic structure of convex polyhedra and higher-dimensional convex polytopes, stating that the graph formed from the vertices and edges of a d-dimensional convex polyhedron or polytope is at least d-vertex-connected, so removing any d minus one vertices leaves the remaining graph connected. Named after Michel Balinski, who published its proof in 1961, the three-dimensional case of the result traces back earlier in the century to Steinitz's theorem characterizing the graphs of three-dimensional polyhedra as the three-connected planar graphs.
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StatementThe skeleton graph formed from the vertices and edges of any d dimensional convex polyhedron or polytope is at least d vertex connected, so removing any fewer than d vertices leaves the remaining graph connected. 1 Classification
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Source Balinski's theorem (Wikipedia)
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Source Michel Balinski (Wikipedia)
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Source Balinski's theorem (Wikipedia)
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1. Balinski's theorem (Wikipedia)
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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.
Proved By: Michel Balinski, Lead sentence
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.
In Branch: Combinatorics, Lead sentence
In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of thr
View the Source Michel Balinski (Wikipedia)
Principal Result Of: Michel Balinski, Body, workQuote, Principal Result Of: Michel Balinski, Body, work
it is known as Balinski's theorem
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