Max cut in cubic graphs
Maximal cut is different from maximum cut (MAX-CUT). In maximum cut, the goal is to find a cut cutting the maximal number of edges. In maximal cut, the goal is to find a local maximum: a cut such that switching the side of any single vertex does not result in more edges being cut. Such a cut exists, since the maximum cut is also maximal. But finding a maximum cut is apparently harder than finding just a maximal cut.