{"paper":{"title":"Clique number of tournaments","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Guillaume Aubian, Pierre Aboulker, Pierre Charbit, Raul Lopes","submitted_at":"2023-10-06T14:11:26Z","abstract_excerpt":"Given a digraph $D$ together with an ordering $\\prec$ of its vertices, the \\emph{backedge graph} of $D$ with respect to $\\prec$ is the undirected graph $D^{\\prec}$ with the same vertex set as $D$, where $xy \\in E(D^{\\prec})$ if $xy \\in A(D)$ and $y \\prec x$. We introduce the notion of the \\emph{clique number of a digraph} $D$, defined as the minimum clique number over all backedge graphs of $D$. We investigate its relationship with the dichromatic number. In particular, this concept allows us to define $\\dic$-bounded classes of digraphs, which constitute the main topic of this paper, with a pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04265","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.04265/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"}