{"paper":{"title":"A dichotomy theorem on the complexity of 3-uniform hypergraphic degree sequence graphicality","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelina Zhang, Arya Maheshwari, Istv\\'an Mikl\\'os, Sara Logsdon","submitted_at":"2024-11-28T10:50:49Z","abstract_excerpt":"We present a dichotomy theorem on the parameterized complexity of the 3-uniform hypergraphicality problem. Given $0<c_1\\le c_2 < 1$, the parameterized 3-uniform Hypergraphic Degree Sequence problem, $3uni-HDS_{c_1,c_2}$, considers degree sequences $D$ of length $n$ such that all degrees are between $c_1 {n-1 \\choose 2}$ and $c_2 {n-1\\choose 2}$ and it asks if there is a 3-uniform hypergraph with degree sequence $D$. We prove that for any $0<c_2< 1$, there exists a unique, polynomial-time computable $c_1^*$ with the following properties. For any $ c_1\\in (c_1^*,c_2]$, $3uni-HDS_{c_1,c_2}$ can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19049","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/2411.19049/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"}