{"paper":{"title":"Transversal Hamilton cycle in hypergraph systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Wang, Donglei Yang, Guanghui Wang, Jie Han, Yangyang Cheng","submitted_at":"2021-11-13T09:53:00Z","abstract_excerpt":"A $k$-graph system $\\textbf{H}=\\{H_i\\}_{i\\in[m]}$ is a family of not necessarily distinct $k$-graphs on the same $n$-vertex set $V$ and a $k$-graph $H$ on $V$ is said to be $\\textbf{H}$-transversal provided that there exists an injection $\\varphi: E(H)\\rightarrow [m]$ such that $e\\in E(H_{\\varphi(e)})$ for all $e\\in E(H)$. We show that given $k\\geq3, \\gamma>0$, sufficiently large $n$ and an $n$-vertex $k$-graph system $\\textbf{H}=\\{H_i\\}_{i\\in[n]}$, if $\\delta_{k-1}(H_i)\\geq(1/2+\\gamma)n$ for each $i\\in[n]$, then there exists an $\\textbf{H}$-transversal tight Hamilton cycle. This extends the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07079","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/2111.07079/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"}