{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T02:26:03Z","timestamp":1791167163072,"version":"4.1.0"},"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 standard bootstrap percolation, a subset $A$ of the grid $[n]^2$ is initially infected. A new site is then infected if at least two of its neighbours are infected, and an infected site stays infected forever. The set $A$ is said to percolate if eventually the entire grid is infected. A percolating set is said to be minimal if none of its subsets percolate. Answering a question of Bollob\u00e1s, we show that there exists a minimal percolating set of size $4n^2\/33 + o(n^2)$, but there does not exist one larger than $(n + 2)^2\/6$.<\/jats:p>","DOI":"10.37236\/91","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:36:57Z","timestamp":1578699417000},"source":"Crossref","is-referenced-by-count":17,"title":["Minimal Percolating Sets in Bootstrap Percolation"],"prefix":"10.37236","volume":"16","author":[{"given":"Robert","family":"Morris","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2009,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:14:49Z","timestamp":1579299289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/91","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1,7]]},"article-number":"R2"}}