Nowhere-Zero \(\vec k\)-Flows on Graphs

Nowhere-Zero \(\vec k\)-Flows on Graphs

We introduce and study a multivariate function that counts nowhere-zero flows on a graph G, in which each edge of G has an individual capacity. We prove that the associated counting function is a piecewise-defined polynomial in these capacities, which satisfy a combinatorial reciprocity law that inc...

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Veröffentlicht in:arXiv.org 2013-05
Hauptverfasser: Beck, Matthias, Cuyjet, Alyssa, Gordon Rojas Kirby, Stubblefield, Molly, Young, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Counting
Polynomials
Reciprocity
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Zusammenfassung:We introduce and study a multivariate function that counts nowhere-zero flows on a graph G, in which each edge of G has an individual capacity. We prove that the associated counting function is a piecewise-defined polynomial in these capacities, which satisfy a combinatorial reciprocity law that incorporates totally cyclic orientations of G.
ISSN:2331-8422