{"paper":{"title":"1-color-avoiding paths, special tournaments, and incidence geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Yang, Jonathan Tidor, Victor Y. Wang","submitted_at":"2016-08-14T23:19:57Z","abstract_excerpt":"We discuss two approaches to a recent question of Loh: must a 3-colored transitive tournament on $N$ vertices have a 1-color-\\emph{avoiding} path of vertex-length at least $N^{2/3}$? This question generalizes the Erd\\H{o}s--Szekeres theorem on monotone subsequences.\n  First, we define three canonical transformations on these tournaments called Color, Record, and Dual. We use these to establish a reduction to special tournaments with natural geometric and combinatorial properties. In many cases (including all known tight examples), these tournaments have recursive Gallai decompositions. Not all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04153","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":""},"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"}