Let G be a minimal imperfect P 5-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 P 4 , cannot induce a bipartite subgraph of G .... As a by-product we also give a structur...

1. Flat, projective, and free modules 1 2. Review of regular local rings 2 3. Cohen-Macauley rings 2 4. The Koszul complex 3 5. The Koszul resolution detects depth 5 6. The detection of depth by use of Ext 6 7. Global dimension 6 8. Minimal resolutions and global dimension 7 9. Serre’s characterization of regular local rings 8 10. The Auslander-Buchsbaum theorem 10 11. Localizations of regular ...