Contractors for flows
Combinatorics
2010-11-30 v1
Abstract
We answer a question raised by Lov\'asz and B. Szegedy [Contractors and connectors in graph algebras, J. Graph Theory 60:1 (2009)] asking for a contractor for the graph parameter counting the number of B-flows of a graph, where B is a subset of a finite Abelian group closed under inverses. We prove our main result using the duality between flows and tensions and finite Fourier analysis. We exhibit several examples of contractors for B-flows, which are of interest in relation to the family of B-flow conjectures formulated by Tutte, Fulkerson, Jaeger, and others.
Cite
@article{arxiv.1011.5958,
title = {Contractors for flows},
author = {Delia Garijo and Andrew Goodall and Jaroslav Nešetřil},
journal= {arXiv preprint arXiv:1011.5958},
year = {2010}
}
Comments
22 pages, 1 figure