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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.4677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-19T17:09:23Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b09b6004d1449a64d0352d258d41085ffb995eac56884e42f62d4d022b3c1bf6","abstract_canon_sha256":"67eead9ada353e028b2a60f1395bb626961b0707509b29ed8154c90e5a0585ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:35.982152Z","signature_b64":"rUlFKXYutBTiKsmh8lALHaRuFCjb96EQ54vbLIHXG6MxFEH3FBPVgFhnMmzdhzRXFVhHNzZW7kdmwh1o/7nDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48666e5ba0ada39d1a60bfc63d847498e306a926ed31578367ce6065661613ef","last_reissued_at":"2026-05-18T02:57:35.981593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:35.981593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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