P_4-laden Graphs: A New Class of Brittle Graphs

Abstract We present a new family of graphs, the family of P4-laden graphs strictly containing the class of P4-lite graphs introduced in (Jamison and Olariu, 1989). We first show that P4-laden graphs are brittle and next, using modular decomposition we present for this class of graphs a linear recognition algorithm as well as linear algorithms for classical optimization problems.