Combinatorial Generation via Permutation Languages. V. Acyclic Orientations

In 1993, Savage, Squire, and West described an inductive construction for generating every acyclic orientation of a chordal graph exactly once, flipping one arc at time. We provide two generalizations this result. First, we describe Gray codes orientations hypergraphs that satisfy simple ordering condition, which generalizes the notion perfect elimination order graphs. This unifies Savage–Squire–West with recent algorithm trees Second, consider quotients lattices graphs, code them, addressing question raised by Pilaud. also lattice congruences weak on symmetric group. Our algorithms are derived from Hartung–Hoang–Mütze–Williams combinatorial generation framework, they yield computing Hamilton paths cycles large classes polytopes, including nestohedra quotientopes. particular, derive efficient implementation construction. Along way, give overview old results about polyhedral order-theoretic aspects graphs hypergraphs.