{"paper":{"title":"Ramsey--Dirac theory for bounded degree hypertrees","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Jaehoon Kim, Jie Han, Seonghyuk Im","submitted_at":"2024-11-27T02:27:23Z","abstract_excerpt":"Ramsey--Tur\\'an theory considers Tur\\'an type questions in Ramsey-context, asking for the existence of a small subgraph in a graph $G$ where the complement $\\overline{G}$ lacks an appropriate subgraph $F$, such as a clique of linear size. Similarly, one can consider Dirac-type questions in Ramsey context, asking for the existence of a spanning subgraph $H$ in a graph $G$ where the complement $\\overline{G}$ lacks an appropriate subgraph $F$, which we call a Ramsey--Dirac theory question.\n  When $H$ is a connected spanning subgraph, the disjoint union $K_{n/2}\\cup K_{n/2}$ of two large cliques s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17996","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/2411.17996/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"}