European Journal of Combinatorics
The lattice structure of flow in planar graphs
SIAM Journal on Discrete Mathematics
Chip-Firing Games on Directed Graphs
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Excluded-minor characterizations of antimatroids arisen from posets and graph searches
Discrete Applied Mathematics
Distributive lattices, polyhedra, and generalized flows
European Journal of Combinatorics
Lattices and maximum flow algorithms in planar graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Lattices generated by Chip Firing Game models: Criteria and recognition algorithms
European Journal of Combinatorics
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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.