{"paper":{"title":"Truncated degree AT-orientations of outerplanar graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chenglong Deng, Xuding Zhu","submitted_at":"2024-12-30T09:07:02Z","abstract_excerpt":"An AT-orientation of a graph $G$ is an orientation $D$ of $G$ such that the number of even Eulerian sub-digraphs and the number of odd Eulerian sub-digraphs of $D$ are distinct. Given a mapping $f: V(G) \\to \\mathbb{N}$, we say $G$ is $f$-AT if $G$ has an AT-orientation $D$ with $ < f(v)$ for each vertex $v$. For a positive integer $k$, we say $G$ is $k$-truncated degree-AT if $G$ is $f$-AT for the mapping $f$ defined as $f(v) = \\min #{k, d_G(v)#} $. This paper proves that 2-connected outerplanar graphs other than odd cycles are $5$-truncated degree-AT, and 2-connected bipartite outerplanar gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20811","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/2412.20811/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"}