A counterexample to the Hirsch conjecture (Q447933)
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scientific article; zbMATH DE number 6074018
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counterexample to the Hirsch conjecture |
scientific article; zbMATH DE number 6074018 |
Statements
A counterexample to the Hirsch conjecture (English)
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30 August 2012
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The Hirsch Conjecture from 1957 states that the graph of a \(d\)-dimensional polytope with \(n\) facets cannot have combinatorial diameter greater than \(n-d\). That is, any two vertices of the polytope can be connected by a path of at most \(n-d\) edges. In this paper this general conjecture is disproved by presenting a counterexample to it. The polytope of the counterexample has dimension \(43\) and \(86\) facets.
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graph diameter
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Hirsch conjecture
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polytopes
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simplex algorithm
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