{"paper":{"title":"Universality for transversal Hamilton cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Candida Bowtell, Katherine Staden, Patrick Morris, Yanitsa Pehova","submitted_at":"2023-10-06T10:22:47Z","abstract_excerpt":"Let $\\mathbf{G}=\\{G_1, \\ldots, G_m\\}$ be a graph collection on a common vertex set $V$ of size $n$ such that $\\delta(G_i) \\geq (1+o(1))n/2$ for every $i \\in [m]$. We show that $\\mathbf{G}$ contains every Hamilton cycle pattern. That is, for every map $\\chi: [n] \\to [m]$ there is a Hamilton cycle whose $i$-th edge lies in $G_{\\chi(i)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04138","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/2310.04138/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"}