Algorithms solving the Matching Cut problem

Abstract

In 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⁎(2n/2)=O⁎(1.4143n) for an n-vertex input graph, and shows that Matching Cut parameterized by the vertex cover number τ(G) can be solved by a single-exponential algorithm in time 2τ(G)O(n2). 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.