{"paper":{"title":"Cyclability of $id$-cycles in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Ruonan Li, Shenggui Zhang","submitted_at":"2016-01-07T04:58:48Z","abstract_excerpt":"Let $G$ be a graph on $n$ vertices and $C'=v_0v_1\\cdots v_{p-1}v_0$ a vertex sequence of $G$ with $p\\geq 3$ ($v_i\\neq v_j$ for all $i,j=0,1,\\ldots,p-1$, $i\\neq j$). If for any successive vertices $v_i$, $v_{i+1}$ on $C'$, either $v_iv_{i+1}\\in E(G)$ or both of the first implicit-degrees of $v_i$ and $v_{i+1}$ are at least $n/2$ (indices are taken modulo $p$), then $C'$ is called an $id$-cycle of $G$. In this paper, we prove that for every $id$-cycle $C'$, there exists a cycle $C$ in $G$ with $V(C')\\subseteq V(C)$. This generalizes several early results on the Hamiltonicity and cyclability of g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01401","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":""},"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"}