{"paper":{"title":"Partitioning ordered hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Dhruv Mubayi, Jacques Verstra\\\"ete, Tao Jiang, Zolt\\'an F\\\" uredi","submitted_at":"2019-06-07T21:57:21Z","abstract_excerpt":"An {\\em ordered $r$-graph} is an $r$-uniform hypergraph whose vertex set is linearly ordered. Given $2\\leq k\\leq r$, an ordered $r$-graph $H$ is {\\em interval} $k$-{\\em partite} if there exist at least $k$ disjoint intervals in the ordering such that every edge of $H$ has nonempty intersection with each of the intervals and is contained in their union.\n  Our main result implies that for each $\\alpha > k - 1$ and $d>0$, every $n$-vertex ordered $r$-graph with $d \\,n^{\\alpha}$ edges has for some $m\\leq n$ an $m$-vertex interval $k$-partite subgraph with $\\Omega(d\\, m^{\\alpha})$ edges. This is an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03342","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/1906.03342/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"}