Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes

DOI10.1007/s11750-013-0292-xzbMath1311.52011OpenAlexW2039678675MaRDI QIDQ5965566

Friedrich Eisenbrand

Publication date: 28 November 2013

Published in: Top (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11750-013-0292-x

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Abstract computational complexity for mathematical programming problems (90C60) Linear programming (90C05) Combinatorial aspects of simplicial complexes (05E45)

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Cites Work

• A counterexample to the Hirsch conjecture
• A linear bound on the diameter of the transportation polytope
• Graphs of transportation polytopes
• An upper bound for the diameter of a polytope
• Random walks, totally unimodular matrices, and a randomised dual simplex algorithm
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• The \(d\)-step conjecture for polyhedra of dimension \(d<6\)
• Diameter of Polyhedra: Limits of Abstraction
• The Hirsch Conjecture for Dual Transportation Polyhedra
• A quasi-polynomial bound for the diameter\\of graphs of polyhedra
• Paths on Polytopes
• On sub-determinants and the diameter of polyhedra