{"paper":{"title":"Chromatic Polynomials and their Zeros and Asymptotic Limits for Families of Graphs","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Robert Shrock","submitted_at":"1999-08-26T17:13:58Z","abstract_excerpt":"Let $P(G,q)$ be the chromatic polynomial for coloring the $n$-vertex graph $G$ with $q$ colors, and define $W=\\lim_{n \\to \\infty}P(G,q)^{1/n}$. Besides their mathematical interest, these functions are important in statistical physics. We give a comparative discussion of exact calculations of $P$ and $W$ for a variety of recursive families of graphs, including strips of regular lattices with various boundary conditions and homeomorphic expansions thereof. Generalizing to $q \\in {\\mathbb C}$, we determine the accumulation sets of the chromatic zeros constituting the continuous loci of points on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9908387","kind":"arxiv","version":2},"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/cond-mat/9908387/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"}