Nowhere-Zero Flow Polynomials
<|reference_start|>Nowhere-Zero Flow Polynomials: In this article we introduce the flow polynomial of a digraph and use it to study nowhere-zero flows from a commutative algebraic perspective. Using Hilbert's Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals. It also yields an appealing proof that every bridgeless triangulated graph has a nowhere-zero four-flow.<|reference_end|>
@article{onn2003nowhere-zero,
    title={Nowhere-Zero Flow Polynomials},
    author={Shmuel Onn},
    journal={Journal of Combinatorial Theory Series A, 108:205--215, 2004},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0309347},
    primaryClass={math.CO cs.DM math.AC}
}