{"paper":{"title":"The Structure of Chromatic Polynomials of Planar Triangulation Graphs and Implications for Chromatic Zeros and Asymptotic Limiting Quantities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Robert Shrock, Yan Xu","submitted_at":"2012-01-20T02:52:48Z","abstract_excerpt":"We present an analysis of the structure and properties of chromatic polynomials $P(G_{pt,\\vec m},q)$ of one-parameter and multi-parameter families of planar triangulation graphs $G_{pt,\\vec m}$, where ${\\vec m} = (m_1,...,m_p)$ is a vector of integer parameters. We use these to study the ratio of $|P(G_{pt,\\vec m},\\tau+1)|$ to the Tutte upper bound $(\\tau-1)^{n-5}$, where $\\tau=(1+\\sqrt{5} \\ )/2$ and $n$ is the number of vertices in $G_{pt,\\vec m}$. In particular, we calculate limiting values of this ratio as $n \\to \\infty$ for various families of planar triangulations. We also use our calcula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4200","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"}