{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:09Z","timestamp":1753893789631,"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>In this note it is proved that if a graph $G$ of order $n$ has an irreducible covering of its vertex set by $n-k$ cliques, then its clique number $\\omega (G)\\leq k+1$ if $k=2$ or 3 and $\\omega (G)\\leq { {k} \\choose {\\lfloor k\/2\\rfloor }}$ if  $k\\geq 4$. These bounds are sharp if $n\\geq k+1$ (for $k=2$ or 3) and  $n\\geq k+ { {k} \\choose {\\lfloor k\/2\\rfloor }}$ (for $k\\geq 4$).<\/jats:p>","DOI":"10.37236\/1672","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:25:09Z","timestamp":1578709509000},"source":"Crossref","is-referenced-by-count":1,"title":["Irreducible Coverings by Cliques and Sperner's Theorem"],"prefix":"10.37236","volume":"9","author":[{"given":"Ioan","family":"Tomescu","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2002,10,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1n11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1n11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:13:13Z","timestamp":1579324393000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1n11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,10,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1672","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,10,22]]},"article-number":"N11"}}