Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
3DCube: A Tool for Three Dimensional Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
On stable cutsets in claw-free graphs and planar graphs
Journal of Discrete Algorithms
A graph drawing based spatial mapping algorithm for coarse-grained reconfigurable architectures
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Computing vertex-surjective homomorphisms to partially reflexive trees
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
QCSP on partially reflexive forests
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
On stable cutsets in claw-free graphs and planar graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
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Finding a cut or finding a matching in a graph are so simple problems that they are hardly considered problems at all. In this paper, by means of a reduction from the NAE3SAT problem, we prove that combining these two problems together, i.e., finding a cut whose split edges are a matching is an NP-complete problem. It remains intractable even if we impose the graph to be simple (no multiple edges allowed) or its maximum degree to be k, with k 驴 4. On the contrary, we give a linear time algorithm that computes a matching-cut of a series-parallel graph. It's open whether the problem is tractable or not for planar graphs.