Abstract
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 ≽ 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.
Research supported in part by the Murst Project: “Algorithms for Large Data Sets”.
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Patrignani, M., Pizzonia, M. (2001). The Complexity of the Matching-Cut Problem. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_26
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DOI: https://doi.org/10.1007/3-540-45477-2_26
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