{"paper":{"title":"On the location of roots of the independence polynomial of bounded degree graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.CO","authors_text":"Pjotr Buys","submitted_at":"2019-03-13T12:55:37Z","abstract_excerpt":"In [1] Peters and Regts confirmed a conjecture by Sokal by showing that for every $\\Delta \\in \\mathbb{Z}_{\\geq 3}$ there exists a complex neighborhood of the interval $\\left[0, \\frac{\\left(\\Delta - 1\\right)^{\\Delta - 1}}{\\left(\\Delta-2\\right)^\\Delta}\\right)$ on which the independence polynomial is nonzero for all graphs of maximum degree $\\Delta$. Furthermore, they gave an explicit neighborhood $U_\\Delta$ containing this interval on which the independence polynomial is nonzero for all finite rooted Cayley trees with branching number $\\Delta$. The question remained whether $U_\\Delta$ would be z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05462","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"}