Graphs whose flow polynomials have only integral roots

Details Graphs whose flow polynomials have only integral roots Graphs whose flow polynomials have only integral roots

2009-08-03

arxiv.org/abs/0908.0181v2

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

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.

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