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Total dual integrality implies local strong unimodularity.(English)Zbl 0633.90061

We prove that any totally dual integral description of a full-dimensional polyhedron is locally strongly unimodular in every vertex.

MSC:

90C27 Combinatorial optimization
52Bxx Polytopes and polyhedra

Cite

References:

[1]R. Chandrasekaran and S. Shirali, ”Total weak modularity: Testing and applications”,Discrete Mathematics 51 (1984) 137–145. ·Zbl 0546.15004 ·doi:10.1016/0012-365X(84)90067-0
[2]W. Cook and W. Pulleyblank, ”Linear systems for constrained matching problems,” to appear inMathematics of Operations Research. ·Zbl 0612.05052
[3]J. Edmonds and R. Giles, ”A min-max relation for submodular functions on graphs”,Annals of Discrete Mathematics 1 (1977) 185–204. ·Zbl 0373.05040 ·doi:10.1016/S0167-5060(08)70734-9
[4]D.R. Fulkerson, ”Blocking and anti-blocking pairs of polyhedra”,Mathematical Programming 1 (1971) 168–194. ·Zbl 0254.90054 ·doi:10.1007/BF01584085
[5]R. Giles and W. Pulleyblank, ”Total dual integrality and integer polyhedra”,Linear Algebra and its Applications 25 (1979) 191–196. ·Zbl 0413.90054 ·doi:10.1016/0024-3795(79)90018-1
[6]A. Hoffman, ”A generalisation of max flow-min cut”,Mathematical Programming 6 (1974) 352–359. ·Zbl 0357.90068 ·doi:10.1007/BF01580250
[7]A. Hoffman and R. Oppenheim, ”Local unimodularity in the matching polytope”,Annals of Discrete Mathematics 2 (1978) 201–209. ·Zbl 0398.90064 ·doi:10.1016/S0167-5060(08)70333-9
[8]A. Schrijver, ”On total dual integrality”,Linear Algebra and its Applications 38 (1981) 27–32. ·Zbl 0474.90065 ·doi:10.1016/0024-3795(81)90005-7
[9]A. Schrijver,Theory of linear and integer programing (Wiley, Chichester, 1986). ·Zbl 0665.90063
[10]A. Sebö,The Schrijver system of odd join polyhedra, Report No. 85394-OR. Institüt für Ökonometrie und Operations Research, Universität Bonn, to appear inCombinatorica.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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