Nowhere-Zero Flow Polynomials

Details Nowhere-Zero Flow Polynomials Nowhere-Zero Flow Polynomials

2003-09-21

arxiv.org/abs/math/0309347v1

Journal of Combinatorial Theory Series A, 108:205--215, 2004

Mathematics

Combinatorics

Scientific paper

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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