{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:28Z","timestamp":1759335928281,"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>We use graceful labellings of paths to give a new way of constructing terraces for cyclic groups. These terraces are then used to find cyclic solutions to the three table Oberwolfach problem, ${\\rm OP}(r,r,s)$, where two of the tables have equal size.  In particular we show that, for every odd $r \\geq 3$ and even $r$ with $4 \\leq r \\leq 16$, there is a number $N_r$ such that there is a cyclic solution to ${\\rm OP}(r,r,s)$ whenever $s \\geq N_r$.  The terraces we are able to construct also prove a conjecture of Anderson: For all $m \\geq 3$, there is a terrace of ${\\Bbb Z}_{2m}$ which begins $0, 2k, k, \\ldots$ for some $k$.<\/jats:p>","DOI":"10.37236\/1955","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:08:55Z","timestamp":1578719335000},"source":"Crossref","is-referenced-by-count":14,"title":["Some Cyclic Solutions to the Three Table Oberwolfach Problem"],"prefix":"10.37236","volume":"12","author":[{"given":"M. A.","family":"Ollis","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,11,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r58\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:06Z","timestamp":1579322406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1955","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,11,15]]},"article-number":"R58"}}