{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:20:53Z","timestamp":1773656453751,"version":"3.50.1"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2015,1,23]],"date-time":"2015-01-23T00:00:00Z","timestamp":1421971200000},"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":[[2016,1]]},"abstract":"<jats:p>We study the expected value of the length<jats:italic>L<jats:sub>n<\/jats:sub><\/jats:italic>of the minimum spanning tree of the complete graph<jats:italic>K<jats:sub>n<\/jats:sub><\/jats:italic>when each edge<jats:italic>e<\/jats:italic>is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that lim<jats:sub><jats:italic>n<\/jats:italic>\u2192\u221e<\/jats:sub><jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548315000024_inline1\"\/><jats:tex-math>$\\mathbb{E}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(<jats:italic>L<jats:sub>n<\/jats:sub><\/jats:italic>) = \u03b6(3) and show that<jats:disp-formula-group><jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0963548315000024_eqnU1\"\/><jats:tex-math>$$ \\mathbb{E}(L_n)=\\zeta(3)+\\frac{c_1}{n}+\\frac{c_2+o(1)}{n^{4\/3}}, $$<\/jats:tex-math><\/jats:alternatives><\/jats:disp-formula><\/jats:disp-formula-group>where<jats:italic>c<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>c<\/jats:italic><jats:sub>2<\/jats:sub>are explicitly defined constants.<\/jats:p>","DOI":"10.1017\/s0963548315000024","type":"journal-article","created":{"date-parts":[[2015,1,23]],"date-time":"2015-01-23T05:09:11Z","timestamp":1421989751000},"page":"89-107","source":"Crossref","is-referenced-by-count":19,"title":["On the Length of a Random Minimum Spanning Tree"],"prefix":"10.1017","volume":"25","author":[{"given":"COLIN","family":"COOPER","sequence":"first","affiliation":[]},{"given":"ALAN","family":"FRIEZE","sequence":"additional","affiliation":[]},{"given":"NATE","family":"INCE","sequence":"additional","affiliation":[]},{"given":"SVANTE","family":"JANSON","sequence":"additional","affiliation":[]},{"given":"JOEL","family":"SPENCER","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,1,23]]},"reference":[{"key":"S0963548315000024_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"S0963548315000024_ref11","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240070406"},{"key":"S0963548315000024_ref9","first-page":"700","volume-title":"Proc. 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