{"paper":{"title":"Rainbow Hamilton cycle in hypergraph system","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Wang, Guanghui Wang, Guiying Yan, Yucong Tang","submitted_at":"2023-01-31T20:23:00Z","abstract_excerpt":"In this paper, we develop a new rainbow Hamilton framework, which is of independent interest, settling the problem proposed by Gupta, Hamann, M\\\"{u}yesser, Parczyk, and Sgueglia when $k=3$, and draw the general conclusion for any $k\\geq3$ as follows. A $k$-graph system $\\textbf{H}=\\{H_i\\}_{i\\in[n]}$ is a family of not necessarily distinct $k$-graphs on the same $n$-vertex set $V$, moreover, a $k$-graph $H$ on $V$ is rainbow if $E(H)\\subseteq \\bigcup_{i\\in[n]}E(H_i)$ and $|E(H)\\cap E(H_i)|\\leq1$ for $i\\in[n]$. We show that given $\\gamma> 0$, sufficiently large $n$ and an $n$-vertex $k$-graph sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00080","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.00080/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"}