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