{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:43Z","timestamp":1753893823557,"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>When $\\Pi$ is a set of $k$ linear orders on a ground set $X$, and $k$ is odd, the $k$-majority tournament generated by $\\Pi$ has vertex set $X$ and has an edge from $u$ to $v$ if and only if a majority of the orders in $\\Pi$ rank $u$ before $v$.  Let $f_k(n)$ be the minimum, over all $k$-majority tournaments with $n$ vertices, of the maximum order of an induced transitive subtournament.  We prove that $f_3(n)\\ge\\sqrt{n}$ always and that $f_3(n)\\le 2\\sqrt{n}-1$ when $n$ is a perfect square.  We also prove that $f_5(n) \\ge n^{1\/4}$.  For general $k$, we prove that $n^{c_k} \\le f_k(n) \\le n^{d_k(n)}$, where $c_k = 3^{-(k-1)\/2}$ and $d_k(n)\\to \\frac{1+\\lg\\lg k}{-1+\\lg k}$ as $n\\to \\infty$.<\/jats:p>","DOI":"10.37236\/609","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:47:00Z","timestamp":1578714420000},"source":"Crossref","is-referenced-by-count":0,"title":["Acyclic Sets in $k$-Majority Tournaments"],"prefix":"10.37236","volume":"18","author":[{"given":"Kevin G.","family":"Milans","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel H.","family":"Schreiber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douglas B.","family":"West","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,5,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p122\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:26Z","timestamp":1579302686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/609","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,5,30]]},"article-number":"P122"}}