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Lattice structure for orientations of graphs - MaRDI portal

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Lattice structure for orientations of graphs

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Publication:6504871

arXivmath/0209005MaRDI QIDQ6504871

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Abstract: Earlier researchers have studied the set of orientations of a connected finite graph G, and have shown that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of local moves of a simple type. Here I show that the set of orientations of G having the same flow-differences around all closed loops can be given the structure of a distributive lattice. The construction generalizes partial orderings that arise in the study of alternating sign matrices. It also gives rise to lattices for the set of degree-constrained factors of a bipartite planar graph; as special cases, one obtains lattices that arise in the study of plane partitions and domino tilings. Lastly, the theory gives a lattice structure to the set of spanning trees of a planar graph.





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