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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.20811","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-12-30T09:07:02Z","cross_cats_sorted":[],"title_canon_sha256":"b3ab6ea899111914e75fec4fe4a479f97bdf503315ac29db4b3c3a93c99fc17c","abstract_canon_sha256":"46ebc5efabbbdf81d47a562af820d11c41aad543dbb42db3d2e17e608043342b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:22.755322Z","signature_b64":"W9eSA+qHDl1bopoLioHXCI7K62I5ofDdNspamBOGbeqb+TSjfi0sVnPE6GYARNFZpG7UnIim/etWhwi5rraQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b565be68450fca7ec5b9a7360922d371d52c223d30fba0b5471ff812329376a1","last_reissued_at":"2026-07-05T09:55:22.754835Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:22.754835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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