{"paper":{"title":"Maximum Modulus of Independence Roots of Graphs and Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Cameron, Jason I.Brown","submitted_at":"2018-12-23T21:17:30Z","abstract_excerpt":"The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size and its roots are called independence roots. We bound the maximum modulus, $\\mbox{maxmod}(n)$, of an independence root over all graphs on $n$ vertices and the maximum modulus, $\\mbox{maxmod}_{T}(n)$, of an independence root over all trees on $n$ vertices in terms of $n$. In particular, we show that\n  $$\\frac{\\log_3(\\mbox{maxmod}(n))}{n}=\\frac{1}{3}+o(1)$$\n  and $$\\frac{\\log_2(\\mbox{maxmod}_{T}(n))}{n}=\\frac{1}{2}+o(1).$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09775","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"}