Establishing the Matching Polytope
نویسنده
چکیده
This paper gives an elementary, inductive proof-" graphical " in spirit-of a theorem of Edmonds' which specifies the convex hull of the matchings of an arbitrary, finite, undirected graph in terms of a fmite system of linear inequalities.
منابع مشابه
On the stable b-matching polytope
We characterize the bipartite stable b-matching polytope in terms of linear constraints. The stable b-matching polytope is the convex hull of the characteristic vectors of stable b-matchings, that is, of stable assignments of a two-sided multiple partner matching model. Our proof uses the comparability theorem of Roth and Sotomayor [13] and follows a similar line as Rothblum did in [14] for the...
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We give a TDI description for a class of polytopes which corresponds to a restricted 2-matching problem. The perfect matching polytope, triangle-free perfect 2-matching polytope and relaxations of the traveling salesman polytope are members of this class. For a class of restrictions G. Cornuéjols, D. Hartvigsen and W.R. Pulleyblank have shown that the unweighted problem is tractable; here we sh...
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We consider the relaxation of the matching polytope defined by the non-negativity and degree constraints. We prove that given an undirected graph on n nodes and the corresponding relaxation of the matching polytope, n /2 iterations of the Lovász-Schrijver semidefinite lifting procedure are needed to obtain the matching polytope, in the worst case. We show that n /2 iterations of the procedu...
متن کاملSeeking a Vertex of the Planar Matching Polytope in NC
For planar graphs, counting the number of perfect matchings (and hence determining whether there exists a perfect matching) can be done in NC [4, 10]. For planar bipartite graphs, finding a perfect matching when one exists can also be done in NC [8, 7]. However in general planar graphs (when the bipartite condition is removed), no NC algorithm for constructing a perfect matching is known. We ad...
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A perfect matching in an undirected graph G = (V,E) is a set of vertex disjoint edges from E that include all vertices in V . The perfect matching problem is to decide if G has such a matching. Recently Rothvoß proved the striking result that the Edmonds’ matching polytope has exponential extension complexity. Here we describe a perfect matching polytope that is different from Edmonds’ polytope...
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