{"paper":{"title":"Chorded pancyclicity in $k$-partite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniela Ferrero, Linda Lesniak","submitted_at":"2018-01-24T04:13:22Z","abstract_excerpt":"We prove that for any integers $p\\geq k\\geq 3$ and any $k$-tuple of positive integers $(n_1,\\ldots ,n_k)$ such that $p=\\sum _{i=1}^k{n_i}$ and $n_1\\geq n_2\\geq \\ldots \\geq n_k$, the condition $n_1\\leq {p\\over 2}$ is necessary and sufficient for every subgraph of the complete $k$-partite graph $K(n_1,\\ldots ,n_k)$ with at least \\[{{4 -2p+2n_1+\\sum _{i=1}^{k} n_i(p-n_i)}\\over 2}\\] edges to be chorded pancyclic. Removing all but one edge incident with any vertex of minimum degree in $K(n_1,\\ldots ,n_k)$ shows that this result is best possible. Our result implies that for any integers, $k\\geq 3$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07854","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"}