{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:51Z","timestamp":1753893831864,"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 score certificate for a tournament, $T$, is a collection of arcs of $T$ which can be uniquely completed to a tournament with the same score-list as $T$'s, and the score certificate number of $T$ is the least number of arcs in a score certificate of $T$. Upper bounds on the score certificate number of upset tournaments are derived.   The upset tournaments on $n$ vertices are in one\u2013to\u2013one correspondence with the ordered partitions of $n-3$, and are \"almost\" transitive tournaments. For each  upset tournament on $n$ vertices a general construction of  a  score certificate with at most  $2n-3$ arcs is given. Also, for the  upset tournament, $T_{\\lambda}$, corresponding to the ordered partition $\\lambda$, a score certificate with at most $n+2k+3$ arcs is constructed, where $k$ is the number of parts of $\\lambda$ of size at least 2. Lower bounds on the score certificate number  of $T_{\\lambda}$ in the case that each part is sufficiently large  are derived. In particular, the score certificate number of the so-called nearly transitive tournament on $n$ vertices is shown to be $n+3$, for $n\\geq 10$.<\/jats:p>","DOI":"10.37236\/1362","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:57:29Z","timestamp":1578707849000},"source":"Crossref","is-referenced-by-count":4,"title":["Short Score Certificates for Upset Tournaments"],"prefix":"10.37236","volume":"5","author":[{"given":"Jeffrey L.","family":"Poet","sequence":"first","affiliation":[]},{"given":"Bryan L.","family":"Shader","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1998,5,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v5i1r24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v5i1r24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:09:29Z","timestamp":1579327769000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v5i1r24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,5,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1998,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1362","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1998,5,5]]},"article-number":"R24"}}