Proceedings of the first Malta conference on Graphs and combinatorics
Handbook of combinatorics (vol. 1)
Matroids: fundamental concepts
Handbook of combinatorics (vol. 1)
The Hilbert zonotope and a polynomial time algorithm for universal Gröbner bases
Advances in Applied Mathematics
Parity, eulerian subgraphs and the Tutte polynomial
Journal of Combinatorial Theory Series B
Expressing combinatorial problems by systems of polynomial equations and hilbert's nullstellensatz
Combinatorics, Probability and Computing
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In this article, we introduce certain flow polynomials associated with digraphs and use them 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.