{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:31Z","timestamp":1753893811466,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The rectangle covering number of an $n$-by-$n$ Boolean matrix $M$ is the smallest number of 1-rectangles which are needed to cover all the 1-entries of $M$. Its binary logarithm is the Nondeterministic Communication Complexity, and it equals the chromatic number of a graph $G(M)$ obtained from $M$ by a construction of Lovasz and Saks.We determine the rectangle covering number and related parameters (clique size, independence ratio, fractional chromatic number of $G(M)$) of random Boolean matrices, where each entry is 1 with probability $p = p(n)$, and the entries are independent.<\/jats:p>","DOI":"10.37236\/5576","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:54:36Z","timestamp":1578671676000},"source":"Crossref","is-referenced-by-count":0,"title":["The Rectangle Covering Number of Random Boolean Matrices"],"prefix":"10.37236","volume":"24","author":[{"given":"Mozhgan","family":"Pourmoradnasseri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dirk Oliver","family":"Theis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2017,6,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:56:29Z","timestamp":1579236989000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/5576","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,6,16]]},"article-number":"P2.37"}}