Saturation numbers for tPk with k less than 6

A graph is called - if does not contain as a subgraph (not necessarily induced) but the addition of any missing edge to creates a copy of . The of , denoted , is the minimum number of edges in an -vertex -saturated graph. Let denote disjoint copies of a path on vertices. For , and sufficiently large, Chen et al. (2015) obtained bounds on and proposed a conjecture on . In this paper, we improve the lower bound on and determine the exact values of for , and , . Moreover, we give some counterexamples for the conjecture of Chen et al. for .