{"paper":{"title":"Tight Bound for Nikiforov's Spectral Even-Cycle Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Feng Liu, Jiasheng Zeng, Peiru Kuang, Shuang Sun, Yan Wang","submitted_at":"2026-06-05T07:25:27Z","abstract_excerpt":"Nikiforov conjectured that, for every fixed $k\\ge2$ and all sufficiently large $n$, the unique $n$-vertex $C_{2k+2}$-free graph with maximum adjacency spectral radius is $S^+_{n,k}$, where $S_{n,k}=K_k\\vee\\overline K_{n-k}$ and $S^+_{n,k}$ is obtained from $S_{n,k}$ by adding one edge inside the independent part. Cioab\\u{a}, Desai and Tait proved this conjecture for $n\\ge k^{O(k)}$. Later, Li and Ning raised the problem of determining the optimal exponent $\\gamma=\\gamma(k)$ such that the same conclusion holds for $n\\ge \\Omega(k^{\\gamma(k)})$.\n  We prove a stronger uniform theorem for Nikiforov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06987","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/2606.06987/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"}