{"paper":{"title":"Extensions of Erd\\H{o}s's 1962 theorem on non-Hamiltonian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Tao Wang, Xu Liu","submitted_at":"2026-04-01T16:05:34Z","abstract_excerpt":"For a positive integer $k$, a graph property $\\mathcal{H}$, and a graph parameter $\\mathcal{P}$, let $\\operatorname{ex}_{\\mathcal{P}}(n, \\mathcal{H}; \\delta \\geq k)$ denote the maximum value of $\\mathcal{P}$ over all $n$-vertex graphs with minimum degree at least $k$ that do not possess the property $\\mathcal{H}$. The corresponding extremal families are denoted by $\\operatorname{EX}_{\\mathcal{P}}(n, \\mathcal{H}; \\delta \\geq k)$. For two disjoint graphs $H_1$ and $H_2$, let $H_1 \\cup H_2$ denote their disjoint union, and let $H_1 \\vee H_2$ denote their join.\n  In 1962, Erd\\H{o}s established a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.01068","kind":"arxiv","version":2},"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/2604.01068/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"}