{"paper":{"title":"On the zero-free region for the chromatic polynomial of graphs with maximum degree $\\Delta$ and girth $g$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aldo Procacci, Emanuel Juliano, Paula M. S. Fialho","submitted_at":"2024-09-20T20:47:30Z","abstract_excerpt":"The purpose of the present paper is to provide, for all pairs of integers $(\\Delta,g)$ with $\\D\\ge 3$ and $g\\ge 3$, a positive number $C(\\Delta, g)$ such that chromatic polynomial $P_G(q)$ of a graph $G$ with maximum degree $\\Delta$ and finite girth $g$ is free of zero if $|q|\\ge C(\\Delta, g)$. Our bounds enlarge the zero-free region in the complex plane of $P_G(q)$ in comparison to previous bounds. In particular, for small values of $\\D$ our estimates yield a sensible improvement on the bounds recently obtained by Jenssen, Patel and Regts in \\cite{JPR}, while they coincide with those of \\cite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13892","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.13892/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}