# Perfectly matchable subgraph problem on a bipartite graph

RAIRO - Operations Research (2010)

- Volume: 44, Issue: 1, page 27-42
- ISSN: 0399-0559

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topSharifov, Firdovsi. "Perfectly matchable subgraph problem on a bipartite graph." RAIRO - Operations Research 44.1 (2010): 27-42. <http://eudml.org/doc/250823>.

@article{Sharifov2010,

abstract = {
We consider the maximum weight perfectly matchable subgraph problem
on a bipartite graph G=(UV,E) with respect to given nonnegative
weights of its edges. We show that G has a perfect matching if and
only if some vector indexed by the nodes in UV is a base of an
extended polymatroid associated with a submodular function defined
on the subsets of UV. The dual problem of the separation problem
for the extended polymatroid is transformed to the special maximum
flow problem on G. In this paper, we give a linear programming
formulation for the maximum weight perfectly matchable subgraph
problem and propose an O(n3) algorithm to solve it.
},

author = {Sharifov, Firdovsi},

journal = {RAIRO - Operations Research},

keywords = {Bipartite graph; extended polymatroid; perfect matching;
perfectly matchable subgraph; bipartite graph; perfectly matchable subgraph},

language = {eng},

month = {2},

number = {1},

pages = {27-42},

publisher = {EDP Sciences},

title = {Perfectly matchable subgraph problem on a bipartite graph},

url = {http://eudml.org/doc/250823},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Sharifov, Firdovsi

TI - Perfectly matchable subgraph problem on a bipartite graph

JO - RAIRO - Operations Research

DA - 2010/2//

PB - EDP Sciences

VL - 44

IS - 1

SP - 27

EP - 42

AB -
We consider the maximum weight perfectly matchable subgraph problem
on a bipartite graph G=(UV,E) with respect to given nonnegative
weights of its edges. We show that G has a perfect matching if and
only if some vector indexed by the nodes in UV is a base of an
extended polymatroid associated with a submodular function defined
on the subsets of UV. The dual problem of the separation problem
for the extended polymatroid is transformed to the special maximum
flow problem on G. In this paper, we give a linear programming
formulation for the maximum weight perfectly matchable subgraph
problem and propose an O(n3) algorithm to solve it.

LA - eng

KW - Bipartite graph; extended polymatroid; perfect matching;
perfectly matchable subgraph; bipartite graph; perfectly matchable subgraph

UR - http://eudml.org/doc/250823

ER -

## References

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- W.H. Cunningham and J. Green-Krotki, A separation algorithm for matchable set polytope. Math. Program.65 (1994) 139–150. Zbl0819.90120
- M. Grotschel, L. Lovasz and A. Schrijver, Geometric algorithms and combinatorial optimization. Springer-Verlag, Berlin (1988). Zbl0634.05001
- F.A. Sharifov, Determination of the minimum cut using the base of an extended polymatroid. Cybern. Syst. Anal.6 (1997) 856–867 (translated from Kibernetika i Systemnyi Analis6 (1996) 138–152, in Russian). Zbl0892.90066

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