منابع مشابه
Establishing the Matching Polytope
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.
متن کاملLower Bounds for Approximating the Matching Polytope
We prove that any extended formulation that approximates the matching polytope on nvertex graphs up to a factor of (1 + ε) for any 2 n ≤ ε ≤ 1 must have at least ( n α/ε ) defining inequalities where 0 < α < 1 is an absolute constant. This is tight as exhibited by the (1 + ε) approximating linear program obtained by dropping the odd set constraints of size larger than (1 + ε)/ε from the descrip...
متن کاملOn 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...
متن کاملEar-decompositions and the complexity of the matching polytope
The complexity of the matching polytope of graphs may be measured with the maximum length β of a starting sequence of odd ears in an ear-decomposition. Indeed, a theorem of Edmonds and Pulleyblank shows that its facets are defined by 2-connected factor-critical graphs, which have an odd ear-decomposition (according to a theorem of Lovász). In particular, β(G) ≤ 1 if and only if the matching pol...
متن کاملOn a Representation of the Matching Polytope Via Semidefinite Liftings
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1972
ISSN: 0095-8956
DOI: 10.1016/0095-8956(72)90002-0