Anti-Path Cover on Sparse Graph Classes
  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. 
Pavel Dvo\v{r}\'ak (Computer Science Institute of Charles University   Charles University Prague, Czech Republic), Du\v{s}an...
cs.DS cs.DM