{"paper":{"title":"Domination in transitive colorings of tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andr\\'as Gy\\'arf\\'as, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","submitted_at":"2013-02-19T17:09:23Z","abstract_excerpt":"An edge coloring of a tournament $T$ with colors $1,2,\\dots,k$ is called \\it $k$-transitive \\rm if the digraph $T(i)$ defined by the edges of color $i$ is transitively oriented for each $1\\le i \\le k$. We explore a conjecture of the second author: For each positive integer $k$ there exists a (least) $p(k)$ such that every $k$-transitive tournament has a dominating set of at most $p(k)$ vertices.\n  We show how this conjecture relates to other conjectures and results. For example, it is a special case of a well-known conjecture of Erd\\H os, Sands, Sauer and Woodrow (so the conjecture is interest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4677","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"}