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A separation algorithm for the matchable set polytope. (English) Zbl 0819.90120

Summary: A matchable set of a graph is a set of vertices joined in pairs by disjoint edges. Balas and Pulleyblank gave a linear-inequality description of the convex hull of matchable sets. We give a polynomial- time combinatorial algorithm for the separation problem for this polytope, and a min-max theorem characterizing the maximum violation by a given point of an inequality of the system.

MSC:

90C35 Programming involving graphs or networks
90C27 Combinatorial optimization
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
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[1] E. Balas and W.R. Pulleyblank, ”The perfectly matchable subgraph polyhedron of an arbitrary graph,”Combinatorica 9 (1989) 495–516. · Zbl 0723.05087 · doi:10.1007/BF02125345
[2] W.H. Cunningham and J. Green-Krótki, ”b-matching degree-sequence polyhedra,”Combinatorica 11 (1991) 219–230. · Zbl 0758.05077 · doi:10.1007/BF01205074
[3] J. Edmonds, ”Maximum matching and a polyhedron with 0–1 vertices,”Journal of Research of the National Bureau of Standards 69B (1965) 126–130. · Zbl 0141.21802
[4] J. Edmonds and E.L. Johnson, ”Matching: A well-solved class of integer linear programs,” in: R.K. Guy et al., eds.Combinatorial Structures and their Applications (Gordon and Breach, New York, 1970) pp. 89–92. · Zbl 0258.90032
[5] A. Frank and E. Tardos, ”An application of simultaneous Diophantine approximation in combinatorial optimization.”Combinatorica 7 (1987) 49–66. · Zbl 0641.90067 · doi:10.1007/BF02579200
[6] M. Grötschel, L. Lovász and A. Schrijver, ”The ellipsoid method and its consequences in combinatorial optimization,”Combinatorica 1 (1981) 169–197. · Zbl 0492.90056 · doi:10.1007/BF02579273
[7] Q. Ning, ”On separation and adjacency problems for perfectly matchable subgraph polytopes of a graph,”Operations Research Letters 6 (1987) 239–242. · Zbl 0625.05038 · doi:10.1016/0167-6377(87)90027-7
[8] M.W. Padberg and M.R. Rao, ”Odd minimum cuts andb-matchings,”Mathematics of Operations Research 7 (1982) 67–80. · Zbl 0499.90056 · doi:10.1287/moor.7.1.67
[9] W.R. Pulleyblank,Faces of Matching Polyhedra, Ph.D. Thesis (University of Waterloo, Ont., Canada, 1973). · Zbl 0318.65027
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