ULD-Lattices and Δ-Bonds
STEFAN FELSNER, KOLJA B. KNAUER
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Source: Crossref
Published: Sep 1, 2009
DOI: 10.1017/s0963548309010001
Open original source ↗Source abstract
We provide a characterization of upper locally distributive lattices (ULD-lattices) in terms of edge colourings of their cover graphs. In many instances where a set of combinatorial objects carries the order structure of a lattice, this characterization yields a slick proof of distributivity or UL-distributivity. This is exemplified by proving a distributive lattice structure on Δ-bonds with invariant circular flow-difference. This instance generalizes several previously studied lattice structures, in particular, c -orientations (Propp), α-orientations of planar graphs (Felsner, resp. de Mendez) and planar flows (Khuller, Naor and Klein). The characterization also applies to other instances, e.g. , to chip-firing games.
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