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. For the matching cut problem, the size of the edge cut also known as the number of crossing edges is a natural parameter.Gomes et al. in \mbox{%DIFAUXCMD Gomes-Sau0pt%DIFAUXCMD showed that MATCHING CUT is FPT when parameterized by maximum size of the edge cutusing a reduction on results provided by Marx et. al \mbox{%DIFAUXCMD marx_treewidth_reduction}0pt%DIFAUXCMD . However,
After revision: In an undirected graph , 0pt%DIFAUXCMD showed that MATCHING CUT is FPT when parameterized by maximum size of the edge cutusing a reduction on results provided by Marx et. al \mbox{%DIFAUXCMD marx_treewidth_reduction}0pt%DIFAUXCMD . However,