{"paper":{"title":"Tournament quasirandomness from local counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Shapira, B. Sudakov, E. Long, M. Buci\\'c","submitted_at":"2019-10-22T12:54:58Z","abstract_excerpt":"A well-known theorem of Chung and Graham states that if $h\\geq 4$ then a tournament $T$ is quasirandom if and only if $T$ contains each $h$-vertex tournament the \"correct number\" of times as a subtournament. In this paper we investigate the relationship between quasirandomness of $T$ and the count of a single $h$-vertex tournament $H$ in $T$. We consider two types of counts, the global one and the local one.\n  We first observe that if $T$ has the correct global count of $H$ and $h \\geq 7$ then quasirandomness of $T$ is only forced if $H$ is transitive. The next natural question when studying q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09936","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/1910.09936/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"}