Lattices generated by Chip Firing Game models: Criteria and recognition algorithms

Authors:
Trung Van Pham;Thi Ha Duong Phan
Affiliations:
-;-
Venue:
European Journal of Combinatorics
Year:
2013

Citing 8
Cited 0

A new polynomial-time algorithm for linear programming

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Balancing vectors in the max norm

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Chip-firing games on graphs

European Journal of Combinatorics
Chip-Firing Games on Directed Graphs

Journal of Algebraic Combinatorics: An International Journal
Chip-Firing and the Critical Group of a Graph

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The lattice structure of chip firing games and related models

Physica D
Classes of lattices induced by chip firing (and sandpile) dynamics

European Journal of Combinatorics
Uld-lattices and Δ-bonds

Combinatorics, Probability and Computing

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Abstract

It is well-known that the class of lattices generated by Chip Firing Games (CFGs) is strictly included in the class of upper locally distributive lattices (ULD). However a necessary and sufficient criterion for this class is still an open question. In this paper we settle this problem by giving such a criterion. This criterion provides a polynomial-time algorithm for constructing a CFG which generates a given lattice if such a CFG exists. Going further we solve the same problem on two other classes of lattices which are generated by CFGs on the classes of undirected graphs and directed acyclic graphs.