{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T20:59:40Z","timestamp":1770325180253,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices $S \\subseteq V(T)$ is a determining set for a tournament $T$ if every nontrivial automorphism of $T$ moves at least one vertex of $S$, while $S$ is a resolving set for $T$ if every two distinct vertices in $T$ have different distances to some vertex in $S$. We show that the minimum size of a determining set for an order $n$ tournament (its determining number) is bounded by $\\lfloor n\/3 \\rfloor$, while the minimum size of a resolving set for an order $n$ strong tournament (its metric dimension) is bounded by $\\lfloor n\/2 \\rfloor$. Both bounds are optimal.<\/jats:p>","DOI":"10.37236\/3182","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:56:37Z","timestamp":1578693397000},"source":"Crossref","is-referenced-by-count":6,"title":["Symmetry Breaking in Tournaments"],"prefix":"10.37236","volume":"20","author":[{"given":"Antoni","family":"Lozano","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p69\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:23:37Z","timestamp":1579242217000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/3182","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3,24]]},"article-number":"P69"}}