{"paper":{"title":"The Removal Lemma for Tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Shapira, Jacob Fox, Lior Gishboliner, Raphael Yuster","submitted_at":"2017-10-15T11:27:17Z","abstract_excerpt":"Suppose one needs to change the direction of at least $\\epsilon n^2$ edges of an $n$-vertex tournament $T$, in order to make it $H$-free. A standard application of the regularity method shows that in this case $T$ contains at least $f^*_H(\\epsilon)n^h$ copies of $H$, where $f^*_H$ is some tower-type function. It has long been observed that many graph/digraph problems become easier when assuming that the host graph is a tournament. It is thus natural to ask if the removal lemma becomes easier if we assume that the digraph $G$ is a tournament.\n  Our main result here is a precise characterization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05317","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":""},"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"}