{"paper":{"title":"On the maximum density of $r$-graphs in which every $(r+1)$-set spans $0$ or $2$ edges","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dhruv Mubayi, Haoran Luo, Vishesh Jain","submitted_at":"2026-06-18T15:30:49Z","abstract_excerpt":"In 1984, Frankl and F\\\"uredi asked for the maximum density of an $n$-vertex $r$-graph in which every $(r+1)$-set of vertices spans $0$ or $2$ edges. They gave a construction with asymptotic density $2^{1-r}$. We significantly improve this bound by constructing such $r$-graphs with density $\\Omega(r^{-3})$, thereby improving the dependence on $r$ from exponential to polynomial. We also obtain lower bounds for the more general problem in which every $(r+1)$-set spans an even number of edges from $\\{0,2,\\ldots,2k\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20367","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/2606.20367/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"}