Nowhere-Zero k→-Flows on Graphs

Nowhere-Zero 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 satisfies a combinatorial reciprocity law that...

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Veröffentlicht in:Annals of combinatorics 2014-12, Vol.18 (4), p.579-583
Hauptverfasser: Beck, Matthias, Cuyjet, Alyssa, Kirby, Gordon Rojas, Stubblefield, Molly, Young, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Mathematics
Mathematics and Statistics
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Beschreibung
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 satisfies a combinatorial reciprocity law that incorporates totally cyclic orientations of G .
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-014-0246-5