Algorithms solving the Matching Cut problem

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 ⁎ ( 2 n / 2 ) = O ⁎ ( 1. 4143 n ) 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 2 τ ( 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.

Authors

• Dieter Kratsch
• Van Bang Le

Keywords

• Matching cut
• Graph algorithm