{"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. We prove that, for every $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00691","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/2606.00691/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"}