ULD-Lattices and Delta-Bonds
Abstract
We provide a characterization of upper locally distributive lattices (ULD-lattices) in terms of edge colorings 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 Delta-bonds with invariant circular flow-difference. This instance generalizes several previously studied lattice structures, in particular, c-orientations (Propp), alpha-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.
Keywords
Cite
@article{arxiv.0807.1217,
title = {ULD-Lattices and Delta-Bonds},
author = {S. Felsner and K. Knauer},
journal= {arXiv preprint arXiv:0807.1217},
year = {2008}
}
Comments
15 pages, 5 figures