{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T19:52:58Z","timestamp":1723233178991},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"We introduce graph-dependent covering arrays which generalize covering arrays on graphs, introduced by Meagher and Stevens (2005), and graph-dependent partition systems, studied by Gargano, K\u00f6rner, and Vaccaro (1994). A covering array $\\hbox{CA}(n; 2, G, H)$ (of strength 2) on column graph $G$ and alphabet graph $H$ is an $n\\times |V(G)|$ array with symbols $V(H)$ such that for every arc $ij \\in E(G)$ and for every arc $ab\\in E(H)$, there exists a \u00a0row $\\vec{r} = (r_{1},\\dots, r_{|V(G)|})$ \u00a0 such that $(r_{i}, r_{j}) = (a,b)$. \u00a0We prove bounds on $n$ when $G$ is a tournament graph and $E(H)$ consists of the edge $(0,1)$, which corresponds to a directed version of Sperner's 1928 theorem. For two infinite families of column graphs, transitive and so-called circular tournaments, we give constructions of covering arrays which are optimal infinitely often.<\/jats:p>","DOI":"10.37236\/6149","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:23:57Z","timestamp":1578669837000},"source":"Crossref","is-referenced-by-count":1,"title":["Binary Covering Arrays on Tournaments"],"prefix":"10.37236","volume":"25","author":[{"given":"Elizabeth","family":"Maltais","sequence":"first","affiliation":[]},{"given":"Lucia","family":"Moura","sequence":"additional","affiliation":[]},{"given":"Mike","family":"Newman","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,6,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:31:20Z","timestamp":1579235480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6149","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,22]]}}}