  A matching cut in a graph G is an edge cut of G that is also a matching. This
short survey gives an overview of old and new results and open problems for
Maximum Matching Cut, which is to determine the size of a largest matching cut
in a graph. We also compare this problem with the related problems Matching
Cut, Minimum Matching Cut, and Perfect Matching Cut, which are to determine if
a graph has a matching cut; the size of a smallest matching cut in a graph; and
if a graph has a matching cut that is a perfect matching, respectively.
Moreover, we discuss a relationship between Maximum Matching Cut and Max Cut,
which is to determine the size of a largest edge cut in a graph, as well as a
relationship between Minimum Matching Cut and Min Cut, which is to determine
the size of a smallest edge cut in a graph.
