{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:16:30Z","timestamp":1773800190285,"version":"3.50.1"},"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 a recent article, Tarnai and G\u00e1sp\u00e1r used computer simulations to find thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius.<\/jats:p>","DOI":"10.37236\/1256","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:25:57Z","timestamp":1578705957000},"source":"Crossref","is-referenced-by-count":36,"title":["Improved Coverings of a Square with Six and Eight Equal Circles"],"prefix":"10.37236","volume":"3","author":[{"given":"J. B. M.","family":"Melissen","sequence":"first","affiliation":[]},{"given":"P. C.","family":"Schuur","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,10,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:15:43Z","timestamp":1579328143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,10,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1256","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,10,22]]},"article-number":"R32"}}