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Chen et al. showed that every connected graph of even order $n$ with no odd $[1,b]$-factor has $A_\\alpha$-spectral radius at most $\\max_{1\\le s\\le k}\\rho_\\alpha(G_s)$, where $G_s=K_s\\nabla\\left(K_{n-(b+1)s-1}\\cup(bs+1)K_1\\right)$ and $k=\\lfloor(n-2)/(b+1)\\rfloor$. Thus the problem reduces to finding the graph with the largest $A_\\alpha$-spectral radius among these obstruction graphs. We prove that, for every $\\"},"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":"2606.00691","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T12:00:32Z","cross_cats_sorted":[],"title_canon_sha256":"5227813711313908a4dac33eb6d5c6fa3fc5925c0b1b8dc1d07c79d20db70f00","abstract_canon_sha256":"073eeda251d04a4fb513f923222a78a4fdb83255951b188972d1cb07ae136e03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:02.821298Z","signature_b64":"ES+mJNOSrjLyuALyF3kGvX85zKd+CutlscXJ8WLumoDON/6fUNoXBzTvReClRAwg+PfmGiVPw7s5JjKXHhbVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b3b7e195617e1c127fce0931eb9fb208ccd1da95662b74e6bcd0a224b10021c","last_reissued_at":"2026-06-02T01:04:02.820846Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:02.820846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp $A_\\alpha$-Spectral Conditions for Odd $[1,b]$-Factors When $\\alpha>1/2$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Silin Huang","submitted_at":"2026-05-30T12:00:32Z","abstract_excerpt":"We solve, for all sufficiently large even orders, the problem proposed by Chen et al. on sharp $A_\\alpha$-spectral conditions for the existence of odd $[1,b]$-factors when $\\alpha>1/2$. Chen et al. showed that every connected graph of even order $n$ with no odd $[1,b]$-factor has $A_\\alpha$-spectral radius at most $\\max_{1\\le s\\le k}\\rho_\\alpha(G_s)$, where $G_s=K_s\\nabla\\left(K_{n-(b+1)s-1}\\cup(bs+1)K_1\\right)$ and $k=\\lfloor(n-2)/(b+1)\\rfloor$. Thus the problem reduces to finding the graph with the largest $A_\\alpha$-spectral radius among these obstruction graphs. 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