Nowhere-Zero Flow Polynomials
Combinatorics
2007-05-23 v1 Discrete Mathematics
Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0309347,
title = {Nowhere-Zero Flow Polynomials},
author = {Shmuel Onn},
journal= {arXiv preprint arXiv:math/0309347},
year = {2007}
}