Tent and a subclass of P5-free graphs

An induced 2K2 of a graph is said to be good if two edges of the 2K2 are at distance three in the graph. In this paper, we give a structural description of the class of all P5-free graphs containing a good 2K2. In particular, we prove that the maximum weight independent set problem for the class of all P5-free graphs containing a good 2K2 can be solved in linear time by proving that every connected graph in this class is a tent which has two disjoint homogeneous sets.