{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833928,"version":"3.41.2"},"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>A $k$-majority tournament is realized by $2k-1$ linear orders on the set of vertices,  where a vertex $u$ dominates $v$ if $u$ precedes $v$ in at least $k$ of the orders.  Various properties of such tournaments have been studied, among them the problem of  finding the size of a smallest dominating set. It is known that $2$-majority tournaments  are dominated by $3$ vertices and that $k$-majority tournaments are dominated by $O(k  \\log k)$ vertices. However, precise values are not known even for $k=3$. We establish  new upper bounds for the size of a smallest dominating set in $k$-majority tournaments  that considerably improve upon previous bounds for small $k$. In particular our result  shows that $3$-majority tournaments are dominated by at most $12$ vertices.<\/jats:p>","DOI":"10.37236\/653","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:05Z","timestamp":1578714185000},"source":"Crossref","is-referenced-by-count":0,"title":["A Recurrence for Bounds on Dominating Sets in $k$-Majority Tournaments"],"prefix":"10.37236","volume":"18","author":[{"given":"Dror","family":"Fidler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,8,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p166\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p166\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:05Z","timestamp":1579302425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p166"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/653","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,8,19]]},"article-number":"P166"}}