An exact algorithm for MAX-CUT in sparse graphs

We study exact algorithms for the MAX-CUT problem. Introducing a new technique, we present an algorithmic scheme that computes a maximum cut in graphs with bounded maximum degree. Our algorithm runs in time O*(2(1-(2/Δ))n)O*(2(1-(2/Δ))n). We also describe a MAX-CUT algorithm for general graphs. Its time complexity is O*(2mn/(m+n))O*(2mn/(m+n)). Both algorithms use polynomial space.