{"paper":{"title":"Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luke Postle, Michelle Delcourt","submitted_at":"2022-04-19T16:32:34Z","abstract_excerpt":"In 1973, Erd\\H{o}s conjectured the existence of high girth $(n,3,2)$-Steiner systems. Recently, Glock, K\\\"{u}hn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erd\\H{o}s' conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erd\\H{o}s' conjecture. As for Steiner systems with more general parameters, Glock, K\\\"{u}hn, Lo, and Osthus conjectured the existence of high girth $(n,q,r)$-Steiner systems. We prove the approximate version of their conjecture.\n  This result follows from our general main results which concern finding perfect or almost perf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.08981","kind":"arxiv","version":3},"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/2204.08981/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"}