Graphs whose flow polynomials have only integral roots
Combinatorics
2009-09-11 v2
Abstract
We show if the flow polynomial of a bridgeless graph G has only integral roots, then G is the dual graph to a planar chordal graph. We also show that for 3-connected cubic graphs, the same conclusion holds under the weaker hypothesis that it has only real flow roots. Expressed in the language of matroid theory, this result says that the cographic matroids with only integral characteristic roots are the cycle matroids of planar chordal graphs.
Keywords
Cite
@article{arxiv.0908.0181,
title = {Graphs whose flow polynomials have only integral roots},
author = {Joseph P. S. Kung and Gordon F. Royle},
journal= {arXiv preprint arXiv:0908.0181},
year = {2009}
}
Comments
12 pages, 1 figure