{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:43:44Z","timestamp":1759063424880,"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 biclique is a complete bipartite subgraph of a graph.  This paper investigates the fractional biclique cover number, $bc^*(G)$, and the fractional biclique partition number, $bp^*(G)$, of a graph $G$.  It is observed that $bc^*(G)$ and $bp^*(G)$ provide lower bounds on the biclique cover and partition numbers respectively, and conditions for equality are given.  It is also shown that $bc^*(G)$ is a better lower bound on the Boolean rank of a binary matrix than the maximum number of isolated ones of the matrix.  In addition, it is noted that $bc^*(G) \\leq bp^*(G) \\leq \\beta^*(G)$, the fractional vertex cover number.  Finally, the application of $bc^*(G)$ and $bp^*(G)$ to two different weak products is discussed.<\/jats:p>","DOI":"10.37236\/1100","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:58:54Z","timestamp":1578718734000},"source":"Crossref","is-referenced-by-count":5,"title":["Fractional Biclique Covers and Partitions of Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Valerie L.","family":"Watts","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r74\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:09:44Z","timestamp":1579320584000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1100","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,8,22]]},"article-number":"R74"}}