Before revision: In an undirected graph  , a matching cut is an edge cut which is also a matching. we refer MATCHING CUT to the problemof deciding if a given graph contain a matching cut or not.
After revision: Given a positive integer d, the d-CUT problem is to decide if an undirected graph , a matching cut is an edge cut which is also a matching. we refer MATCHING CUT to the problemof deciding if a given graph contain a matching cut or not.