{"paper":{"title":"Tighter Bounds on the Degree-Truncated Choice Number of Planar Graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huan Zhou, Huijuan Xu, Jialu Zhu, Xuding Zhu","submitted_at":"2026-06-04T14:30:45Z","abstract_excerpt":"Assume $G$ is a graph and $k$ is a positive integer. Let $f:V(G)\\to \\mathbb{N}$ be defined as $f(v)=\\min\\{k,d_G(v)\\}$. If $G$ is $f$-choosable, then we say $G$ is degree-truncated $k$-choosable. The degree-truncated choice number of $G$ is $\\operatorname{ch}^{\\text{\\st{d}}}(G) = \\min\\{k: G \\text{ is degree-truncated $k$-choosable}\\}$. For a family $\\mathcal{G}$ of graphs, $\\operatorname{ch}^{\\text{\\st{d}}}(\\mathcal{G}) = \\max\\{\\operatorname{ch}^{\\text{\\st{d}}}(G):G \\in \\mathcal{G}\\}$. Let $\\mathcal{P}$ denote the family of 3-connected non-complete planar graphs. Richter asked in 2008 whether $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06216","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/2606.06216/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"}