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Real-rooted flow polynomials have only integral roots
Abstract
Let G be a connected bridgeless graph. In 2011, Kung and Royle showed that all roots of the flow polynomial F(G,λ) of G are integers if and only if G is the dual of a chordal plane graph. In this article, we further prove that if F(G,λ) has real roots only, then G is the dual of a chordal plane graph and each root of F(G,λ) is an integer in the set {1,2,3}.
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BibTeX
@misc{zhang2026realrooted,
title = {{Real-rooted flow polynomials have only integral roots}},
author = {Meiqiao Zhang and Fengming Dong},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.19780},
eprint = {2608.19780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19780},
}
RIS
TY - UNPB
TI - Real-rooted flow polynomials have only integral roots
AU - Meiqiao Zhang
AU - Fengming Dong
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.19780
UR - https://arxiv.org/abs/2608.19780
AB - Let G be a connected bridgeless graph. In 2011, Kung and Royle showed that all roots of the flow polynomial F(G,λ) of G are integers if and only if G is the dual of a chordal plane graph. In this article, we further prove that if F(G,λ) has real roots only, then G is the dual of a chordal plane graph and each root of F(G,λ) is an integer in the set {1,2,3}.
ER -