Abstract
AbstractIn a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete. This paper provides a first branching algorithm solving Matching Cut in time \(O^*(2^{n/2})=O^*(1.4143^n)\) for an \(n\)-vertex input graph, and shows that Matching Cut parameterized by vertex cover number \(\tau (G)\) can be solved by a single-exponential algorithm in time \(2^{\tau (G)} O(n^2)\). Moreover, the paper also gives a polynomially solvable case for Matching Cut which covers previous known results on graphs of maximum degree three, line graphs, and claw-free graphs.
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