On minimal cutsets in P5-free minimal imperfect graphs Original Research Article

Let G be a minimal imperfect P5-free graph (i.e. a minimal imperfect graph not containing a path on 5 vertices as induced subgraph) and let S be a minimal cutset of G. In this paper we study several properties of such cutsets, in particular we prove that the subgraph induced by S is connected, contains a P4, cannot induce a bipartite subgraph of G,… . As a by-product we also give a structural characterization of such graphs.