{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T10:51:22Z","timestamp":1771843882345,"version":"3.50.1"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2017,10,9]],"date-time":"2017-10-09T00:00:00Z","timestamp":1507507200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:p>Assume that the edges of the complete graph<jats:italic>K<jats:sub>n<\/jats:sub><\/jats:italic>are given independent uniform [0, 1] weights. We consider the expected minimum total weight<jats:italic>\u03bc<jats:sub>k<\/jats:sub><\/jats:italic>of<jats:italic>k<\/jats:italic>\u2a7d 2 edge-disjoint spanning trees. When<jats:italic>k<\/jats:italic>is large we show that<jats:italic>\u03bc<jats:sub>k<\/jats:sub><\/jats:italic>\u2248<jats:italic>k<\/jats:italic><jats:sup>2<\/jats:sup>. Most of the paper is concerned with the case<jats:italic>k<\/jats:italic>= 2. We show that<jats:italic>m<\/jats:italic><jats:sub>2<\/jats:sub>tends to an explicitly defined constant and that<jats:italic>\u03bc<\/jats:italic><jats:sub>2<\/jats:sub>\u2248 4.1704288.\u00a0.\u00a0.\u00a0.<\/jats:p>","DOI":"10.1017\/s0963548317000426","type":"journal-article","created":{"date-parts":[[2017,10,9]],"date-time":"2017-10-09T00:43:25Z","timestamp":1507509805000},"page":"228-244","source":"Crossref","is-referenced-by-count":4,"title":["On Edge-Disjoint Spanning Trees in a Randomly Weighted Complete Graph"],"prefix":"10.1017","volume":"27","author":[{"given":"ALAN","family":"FRIEZE","sequence":"first","affiliation":[]},{"given":"TONY","family":"JOHANSSON","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,10,9]]},"reference":[{"key":"S0963548317000426_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009825"},{"key":"S0963548317000426_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s11511-010-0046-7"},{"key":"S0963548317000426_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(87)90047-3"},{"key":"S0963548317000426_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548399003892"},{"key":"S0963548317000426_ref21","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1662"},{"key":"S0963548317000426_ref19","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20147"},{"key":"S0963548317000426_ref17","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240070406"},{"key":"S0963548317000426_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02125348"},{"key":"S0963548317000426_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(85)90058-7"},{"key":"S0963548317000426_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548315000024"},{"key":"S0963548317000426_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80030-8"},{"key":"S0963548317000426_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579431"},{"key":"S0963548317000426_ref27","volume-title":"Matroid Theory","author":"Oxley","year":"1992"},{"key":"S0963548317000426_ref6","first-page":"469","volume-title":"SODA 2007: Proc. 18th Annual ACM\u2013SIAM Symposium on Discrete Algorithms","author":"Cain","year":"2007"},{"key":"S0963548317000426_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(85)90059-9"},{"key":"S0963548317000426_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90171-8"},{"key":"S0963548317000426_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01192719"},{"key":"S0963548317000426_ref15","doi-asserted-by":"crossref","first-page":"R41","DOI":"10.37236\/1519","article-title":"A note on random minimum length spanning trees","volume":"7","author":"Frieze","year":"2000","journal-title":"Electron. J. Combin."},{"key":"S0963548317000426_ref28","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199801)12:1<63::AID-RSA4>3.0.CO;2-R"},{"key":"S0963548317000426_ref33","volume-title":"Matroid Theory","author":"Welsh","year":"1976"},{"key":"S0963548317000426_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-003-0308-9"},{"key":"S0963548317000426_ref8","volume-title":"Probability: Theory and Examples","author":"Durrett","year":"1991"},{"key":"S0963548317000426_ref20","doi-asserted-by":"publisher","DOI":"10.1137\/0208045"},{"key":"S0963548317000426_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005773"},{"key":"S0963548317000426_ref29","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0036"},{"key":"S0963548317000426_ref24","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20084"},{"key":"S0963548317000426_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.1015"},{"key":"S0963548317000426_ref31","doi-asserted-by":"publisher","DOI":"10.1214\/ECP.v14-1475"},{"key":"S0963548317000426_ref26","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-39.1.12"},{"key":"S0963548317000426_ref16","doi-asserted-by":"crossref","unstructured":"Gao P. , P\u00e9rez-Gim\u00e9nez X. and Sato C. M. (2014) Arboricity and spanning-tree packing in random graphs with an application to load balancing. Extended abstract published in SODA 2014, pp. 317\u2013326.","DOI":"10.1137\/1.9781611973402.23"},{"key":"S0963548317000426_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90162-U"},{"key":"S0963548317000426_ref25","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-36.1.445"},{"key":"S0963548317000426_ref12","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1040.0105"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548317000426","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,18]],"date-time":"2020-10-18T22:32:28Z","timestamp":1603060348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548317000426\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,9]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["S0963548317000426"],"URL":"https:\/\/doi.org\/10.1017\/s0963548317000426","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,9]]}}}