Loose vertices in C4-free Berge graphs Original Research Article

Following Maire (Graphs Combin. 10 (3) (1994) 263) we call a loose vertex a vertex whose neighbourhood induces a P4-free graph, and we show that every C4-free Berge graph G which is not a clique either is breakable (i.e. G or Ḡ has a star-cutset) or contains at least two non-adjacent loose vertices. Consequently, every minimal imperfect C4-free graph has loose vertices.