{"paper":{"title":"On Zero-free Intervals of Flow Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fengming Dong","submitted_at":"2014-03-08T01:46:59Z","abstract_excerpt":"This article studies real roots of the flow polynomial $F(G,\\lambda)$ of a bridgeless graph $G$. For any integer $k\\ge 0$, 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 $k\\le 2$, $\\xi_3=1.430\\cdots$, $\\xi_4=1.361\\cdots$ and $\\xi_5=1.317\\cdots$. We also prove that for any bridgeless graph $G=(V,E)$, if all roots of $F(G,\\lambda)$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1916","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}