# Maximum Semi-Matching Problem in Bipartite Graphs

• Volume: 33, Issue: 3, page 559-569
• ISSN: 2083-5892

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## Abstract

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An (f, g)-semi-matching in a bipartite graph G = (U ∪ V,E) is a set of edges M ⊆ E such that each vertex u ∈ U is incident with at most f(u) edges of M, and each vertex v ∈ V is incident with at most g(v) edges of M. In this paper we give an algorithm that for a graph with n vertices and m edges, n ≤ m, constructs a maximum (f, g)-semi-matching in running time O(m ⋅ min [...] ) Using the reduction of [5] our result on maximum (f, g)-semi-matching problem directly implies an algorithm for the optimal semi-matching problem with running time O( [...] log n).

## How to cite

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Ján Katrenič, and Gabriel Semanišin. "Maximum Semi-Matching Problem in Bipartite Graphs." Discussiones Mathematicae Graph Theory 33.3 (2013): 559-569. <http://eudml.org/doc/267689>.

@article{JánKatrenič2013,
abstract = {An (f, g)-semi-matching in a bipartite graph G = (U ∪ V,E) is a set of edges M ⊆ E such that each vertex u ∈ U is incident with at most f(u) edges of M, and each vertex v ∈ V is incident with at most g(v) edges of M. In this paper we give an algorithm that for a graph with n vertices and m edges, n ≤ m, constructs a maximum (f, g)-semi-matching in running time O(m ⋅ min [...] ) Using the reduction of [5] our result on maximum (f, g)-semi-matching problem directly implies an algorithm for the optimal semi-matching problem with running time O( [...] log n).},
author = {Ján Katrenič, Gabriel Semanišin},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {semi-matching; quasi-matching; bipartite graph; computational complexity},
language = {eng},
number = {3},
pages = {559-569},
title = {Maximum Semi-Matching Problem in Bipartite Graphs},
url = {http://eudml.org/doc/267689},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Ján Katrenič
AU - Gabriel Semanišin
TI - Maximum Semi-Matching Problem in Bipartite Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 3
SP - 559
EP - 569
AB - An (f, g)-semi-matching in a bipartite graph G = (U ∪ V,E) is a set of edges M ⊆ E such that each vertex u ∈ U is incident with at most f(u) edges of M, and each vertex v ∈ V is incident with at most g(v) edges of M. In this paper we give an algorithm that for a graph with n vertices and m edges, n ≤ m, constructs a maximum (f, g)-semi-matching in running time O(m ⋅ min [...] ) Using the reduction of [5] our result on maximum (f, g)-semi-matching problem directly implies an algorithm for the optimal semi-matching problem with running time O( [...] log n).
LA - eng
KW - semi-matching; quasi-matching; bipartite graph; computational complexity
UR - http://eudml.org/doc/267689
ER -

## References

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