English

Nowhere-Zero $\vec k$-Flows on Graphs

Combinatorics 2016-05-10 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1305.2456,
  title  = {Nowhere-Zero $\vec k$-Flows on Graphs},
  author = {Matthias Beck and Alyssa Cuyjet and Gordon Rojas Kirby and Molly Stubblefield and Michael Young},
  journal= {arXiv preprint arXiv:1305.2456},
  year   = {2016}
}

Comments

4 pages, 1 figure

R2 v1 2026-06-22T00:14:48.628Z