Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 04, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Hung Hoang (Amazon)

Zigzagging through acyclic orientations of graphs and hypergraphs

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 a time. In this talk, I will mention two generalizations of this result. The first is Gray codes for acyclic orientations of hypergraphs that satisfy a simple ordering condition, which generalizes the notion of perfect elimination order of chordal graphs. This unifies the Savage-Squire-West construction with a recent algorithm for generating elimination trees of chordal graphs. Secondly, the second generalization is a Gray code for the quotients of lattices of acyclic orientations of chordal graphs, addressing a question raised by Pilaud (2022). This also generalizes a recent algorithm for generating lattice congruences of the weak order on the symmetric group. The algorithms are derived from the Hartung-Hoang-Mütze-Williams combinatorial generation framework, and they yield simple algorithms for computing Hamilton paths and cycles on large classes of polytopes, including chordal nestohedra and quotientopes.

Joint work with Jean Cardinal, Arturo Merino, Ondřej Mička, and Torsten Mütze.

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