{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830877,"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>An unsatisfiable formula is called minimal if it becomes satisfiable whenever any of its clauses are removed. We construct minimal unsatisfiable $k$-SAT formulas with $\\Omega(n^k)$ clauses for $k \\geq 3$, thereby negatively answering a question of Rosenfeld. This should be compared to the result of Lov\u00e1sz [Studia Scientiarum Mathematicarum Hungarica 11, 1974, p113-114] which asserts that a critically 3-chromatic $k$-uniform hypergraph can have at most ${n\\choose k-1}$ edges.<\/jats:p>","DOI":"10.37236\/241","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:36:12Z","timestamp":1578717372000},"source":"Crossref","is-referenced-by-count":2,"title":["On the Size of Minimal Unsatisfiable Formulas"],"prefix":"10.37236","volume":"16","author":[{"given":"Choongbum","family":"Lee","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,1,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:13:06Z","timestamp":1579317186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/241","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,1,30]]},"article-number":"N3"}}