Disjoint paths and connected subgraphs for H-free graphs

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting different terminal pair from set of distinct vertex pairs. We determine, with an exception two cases, the complexity for H -free graphs. If fixed, we obtain -Disjoint problem, which known be polynomial-time solvable on class all graphs every ? 1 . latter does no longer hold need connect vertices sets instead completely classify Connected Subgraphs graphs, and give same almost-complete classification as Moreover, exact algorithms n m edges that have running times O ( 2 ) 3 , respectively.