Abstract
In an undirected graph, a matching cut is a partition of vertices into two sets such that the edges across the sets induce a matching. The matching cut problem is the problem of deciding whether a given graph has a matching cut. The matching cut problem can be expressed using a monadic second-order logic (MSOL) formula and hence is solvable in linear time for graphs with bounded tree-width. However, this approach leads to a running time of \(f(\phi , t) n^{O(1)}\), where \(\phi \) is the length of the MSOL formula, t is the tree-width of the graph and n is the number of vertices of the graph.
In [Theoretical Computer Science, 2016], Kratsch and Le asked to give a single exponential algorithm for the matching cut problem with tree-width alone as the parameter. We answer this question by giving a \(2^{O(t)} n^{O(1)}\) time algorithm. We also show the tractability of the matching cut problem when parameterized by neighborhood diversity and other structural parameters.
Anjeneya Swami Kare—Faculty member of University of Hyderabad.
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Aravind, N.R., Kalyanasundaram, S., Kare, A.S. (2017). On Structural Parameterizations of the Matching Cut Problem. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_34
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DOI: https://doi.org/10.1007/978-3-319-71147-8_34
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