Partitioning to three matchings of given size is NP-complete for bipartite graphs
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 conta...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2014-12-01
|
| Series: | Acta Universitatis Sapientiae: Informatica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ausi-2015-0004 |
| Summary: | 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. |
|---|---|
| ISSN: | 2066-7760 |