{"paper":{"title":"Graph Polynomials and Group Coloring of Graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bart{\\l}omiej Bosek, Grzegorz Gutowski, Jaros{\\l}aw Grytczuk, Mariusz Zaj\\k{a}c, Oriol Serra","submitted_at":"2020-12-06T10:46:44Z","abstract_excerpt":"Let $\\Gamma$ be an Abelian group and let $G$ be a simple graph. We say that $G$ is $\\Gamma$-colorable if for some fixed orientation of $G$ and every edge labeling $\\ell:E(G)\\rightarrow \\Gamma$, there exists a vertex coloring $c$ by the elements of $\\Gamma$ such that $c(y)-c(x)\\neq \\ell(e)$, for every edge $e=xy$ (oriented from $x$ to $y$).\n  Langhede and Thomassen proved recently that every planar graph on $n$ vertices has at least $2^{n/9}$ different $\\mathbb{Z}_5$-colorings. By using a different approach based on graph polynomials, we extend this result to $K_5$-minor-free graphs in the more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03230","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/2012.03230/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"}