{"paper":{"title":"Distinguishing Tournaments with Small Label Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antoni Lozano","submitted_at":"2017-07-18T10:14:53Z","abstract_excerpt":"A $d$-distinguishing vertex (arc) labeling of a digraph is a vertex (arc) labeling using $d$ labels that is not preserved by any nontrivial automorphism. Let $\\rho(T)$ ($\\rho'(T)$) be the minimum size of a label class in a 2-distinguishing vertex (arc) labeling of a tournament $T$. Gluck's Theorem implies that $\\rho(T) \\le \\lfloor n/2 \\rfloor$ for any tournament $T$ of order $n$. In this paper we construct a family of tournaments $\\cal H$ such that $\\rho(T) \\ge \\lfloor n/2 \\rfloor$ for any order $n$ tournament in $\\cal H$. Additionally, we prove that $\\rho'(T) \\le \\lfloor 7n/36 \\rfloor + 3$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05549","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"}