Partitioning to three matchings of given size is NP-complete for bipartite graphs
2014 ◽
Vol 6
(2)
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pp. 206-209
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Abstract We show that the problem of deciding whether the edge set of a bipartite graph can be partitioned into three matchings, of size k1, k2 and k3 is NP-complete, even if one of the matchings is required to be perfect. We also show that the problem of deciding whether the edge set of a simple graph contains a perfect matching and a disjoint matching of size k or not is NP-complete, already for bipartite graphs with maximum degree 3. It also follows from our construction that it is NP-complete to decide whether in a bipartite graph there is a perfect matching and a disjoint matching that covers all vertices whose degree is at least 2.
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2013 ◽
Vol 22
(5)
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pp. 783-799
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2014 ◽
Vol Vol. 16 no. 3
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2020 ◽
Vol 54
(3 (253))
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pp. 137-145
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