Work

Real-rooted flow polynomials have only integral roots

Year: 2026

Type: preprint

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 $\{1,2,3\}$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.19780

Authors: Zhang, Meiqiao, Dong, Fengming

Institutions: Xiamen University, Nanyang Technological University, National Institute of Education

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203861103

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