{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T21:40:20Z","timestamp":1697665220303},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2002,7,10]],"date-time":"2002-07-10T00:00:00Z","timestamp":1026259200000},"content-version":"unspecified","delay-in-days":70,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2002,5]]},"abstract":"Let c<\/jats:italic> [les ] 0.076122 and T<\/jats:italic>1<\/jats:sub>, T<\/jats:italic>2<\/jats:sub>,\u2026, T<\/jats:italic>n<\/jats:italic><\/jats:sub> be a sequence of trees such that \n[mid ]V<\/jats:italic>(T<\/jats:italic>i<\/jats:sub>)[mid ] [les ] i<\/jats:italic>\u2212c<\/jats:italic>(i<\/jats:italic>\u22121). \nWe prove that, if for each 1 [les ] i<\/jats:italic> [les ] n<\/jats:italic> there exists a vertex x<\/jats:italic>i<\/jats:sub> \u2208 V<\/jats:italic>(T<\/jats:italic>i<\/jats:italic><\/jats:sub>) such that T<\/jats:italic>i<\/jats:italic><\/jats:sub>\u2212x<\/jats:italic>i<\/jats:italic><\/jats:sub> has at least (1\u22122c<\/jats:italic>)(i<\/jats:italic>\u22121) isolated vertices, then T<\/jats:italic>1<\/jats:sub>,\u2026, T<\/jats:italic>n<\/jats:italic><\/jats:sub> can be packed into K<\/jats:italic>n<\/jats:italic><\/jats:sub>. We also prove that if T<\/jats:italic> is a tree of order n<\/jats:italic>+1\u2212c<\/jats:italic>\u2032n<\/jats:italic>, c<\/jats:italic>\u2032 [les ] \n1\/25\n(37\u22128 \n\u221a21\n) \u2248 0.0135748, such that there exists a vertex x<\/jats:italic> \u2208 V<\/jats:italic>(T<\/jats:italic>) and T<\/jats:italic>\u2212x<\/jats:italic> has at least n<\/jats:italic>(1\u22122c<\/jats:italic>\u2032) isolated vertices, then 2n<\/jats:italic>+1 copies of T<\/jats:italic> may be packed into K<\/jats:italic>2n<\/jats:italic>+1<\/jats:sub>.<\/jats:p>","DOI":"10.1017\/s0963548301005077","type":"journal-article","created":{"date-parts":[[2002,7,28]],"date-time":"2002-07-28T19:18:00Z","timestamp":1027883880000},"page":"263-272","source":"Crossref","is-referenced-by-count":6,"title":["Packing Trees into \nthe Complete Graph"],"prefix":"10.1017","volume":"11","author":[{"given":"EDWARD","family":"DOBSON","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2002,7,10]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548301005077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,30]],"date-time":"2019-03-30T15:21:45Z","timestamp":1553959305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548301005077\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,5]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,5]]}},"alternative-id":["S0963548301005077"],"URL":"https:\/\/doi.org\/10.1017\/s0963548301005077","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,5]]}}}