  We show that it is possible to use Bondy-Chvatal closure to design an FPT
algorithm that decides whether or not it is possible to cover vertices of an
input graph by at most k vertex disjoint paths in the complement of the input
graph. More precisely, we show that if a graph has tree-width at most w and its
complement is closed under Bondy-Chvatal closure, then it is possible to bound
neighborhood diversity of the complement by a function of w only. A simpler
proof where tree-depth is used instead of tree-width is also presented.
