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Nowhere-Zero Flow Polynomials

Shmuel Onn
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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.

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Shmuel Onn. 2003-09-21. Nowhere-Zero Flow Polynomials. https://arxiv.org/abs/math/0309347

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