{"paper":{"title":"Extremal problems on the Hamiltonicity of claw-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning, Xing Peng","submitted_at":"2015-04-16T11:58:17Z","abstract_excerpt":"In 1962, Erd\\H{o}s proved that if a graph $G$ with $n$ vertices satisfies $$ e(G)>\\max\\left\\{\\binom{n-k}{2}+k^2,\\binom{\\lceil(n+1)/2\\rceil}{2}+\\left\\lfloor \\frac{n-1}{2}\\right\\rfloor^2\\right\\}, $$ where the minimum degree $\\delta(G)\\geq k$ and $1\\leq k\\leq(n-1)/2$, then it is Hamiltonian. For $n \\geq 2k+1$, let $E^k_n=K_{k}\\vee (kK_1+K_{n-2k})$, where \"$\\vee$\" is the \"join\" operation. One can observe $e(E^k_n)=\\binom{n-k}{2}+k^2$ and $E^k_n$ is not Hamiltonian. As $E^k_n$ contains induced claws for $k\\geq 2$, a natural question is to characterize all 2-connected claw-free non-Hamiltonian graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04195","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}