Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice structure for orientations of graphs   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.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph