Bases, reorientations, and linear programming, in uniform and rank-3 oriented matroids

DOI10.1016/S0196-8858(03)00081-2zbMath1053.05023MaRDI QIDQ1433002

Michel Las Vergnas, Emeric Gioan

Publication date: 15 June 2004

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Linear programmingTutte polynomialOrientationMatroidBijective proofOriented matroidBasisAcyclic orientationBasis activityPseudolinePseudoline arrangement

Mathematics Subject Classification ID

Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Linear programming (90C05) Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items

External and internal elements of a matroid basis, Fully Optimal Bases and the Active Bijection in Graphs, Hyperplane Arrangements, and Oriented Matroids, Computing the fully optimal spanning tree of an ordered bipolar directed graph, The active bijection for graphs, The active bijection in graphs, hyperplane arrangements, and oriented matroids, 1: the fully optimal basis of a bounded region, Activity preserving bijections between spanning trees and orientations in graphs

Cites Work

• Convexity in oriented matroids
• Acyclic and totally cyclic orientations of combinatorial geometries
• External and internal elements of a matroid basis
• The Tutte polynomial
• Acyclic orientations of graphs
• Activity preserving bijections between spanning trees and orientations in graphs
• On the Interpretation of Whitney Numbers Through Arrangements of Hyperplanes, Zonotopes, Non-Radon Partitions, and Orientations of Graphs
• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• Oriented Matroids
• A Contribution to the Theory of Chromatic Polynomials
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