Graphs whose flow polynomials have only integral roots
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 3connected 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 DOI:
 10.48550/arXiv.0908.0181
 arXiv:
 arXiv:0908.0181
 Bibcode:
 2009arXiv0908.0181K
 Keywords:

 Mathematics  Combinatorics;
 05B35
 EPrint:
 12 pages, 1 figure