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- W1991662488 abstract "This article studies real roots of the flow polynomial $F(G,lambda)$ of a bridgeless graph $G$. For any integer $kge 0$, let $xi_k$ be the supremum in $(1,2]$ such that $F(G,lambda)$ has no real roots in $(1,xi_k)$ for all graphs $G$ with $|W(G)|le k$, where $W(G)$ is the set of vertices in $G$ of degrees larger than $3$. We prove that $xi_k$ can be determined by considering a finite set of graphs and show that $xi_k=2$ for $kle 2$, $xi_3=1.430cdots$, $xi_4=1.361cdots$ and $xi_5=1.317cdots$. We also prove that for any bridgeless graph $G=(V,E)$, if all roots of $F(G,lambda)$ are real but some of these roots are not in the set ${1,2,3}$, then $|E|ge |V|+17$ and $F(G,lambda)$ has at least 9 real roots in $(1,2)$." @default.
- W1991662488 created "2016-06-24" @default.
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- W1991662488 date "2015-03-01" @default.
- W1991662488 modified "2023-09-29" @default.
- W1991662488 title "On zero-free intervals of flow polynomials" @default.
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- W1991662488 doi "https://doi.org/10.1016/j.jctb.2014.11.001" @default.
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