This paper is intended to give a concise understanding
of the facial structure of previously separately
investigated polyhedra. We introduce the notion of
transitive packing and the transitive packing
polytope and give cutting plane proofs for huge
classes of valid inequalities of this polytope. We
introduce generalized cycle, generalized clique,
generalized antihole, generalized antiweb,
generalized web, and odd partition
inequalities. These classes subsume several known
classes of valid inequalities for several of the
special cases but also give many new inequalities
for several others. For some of the classes we also
prove a nontrivial lower bound for their Chvátal
rank. Finally, we relate the concept of transitive
packing to generalized (set) packing and covering as
well as to balanced and ideal matrices.
