{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T22:44:45Z","timestamp":1780613085236,"version":"3.54.1"},"reference-count":9,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5793,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1990,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Grow a tree on <jats:italic>n<\/jats:italic> vertices by starting with no edges and successively adding an edge chosen uniformly from the set of possible edges whose addition would not create a cycle. This process is closely related to the classical random graph process. We describe the asymptotic structure of the tree, as seen locally from a given vertex. In particular, we give an explicit expression for the asymptotic degree distribution. Our results an be applied to study the random minimum\u2010weight spanning tree question, when the edge\u2010weight distribution is allowed to vary almost arbitrarily with <jats:italic>n<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/rsa.3240010402","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T08:20:19Z","timestamp":1180599619000},"page":"383-402","source":"Crossref","is-referenced-by-count":45,"title":["A random tree model associated with random graphs"],"prefix":"10.1002","volume":"1","author":[{"given":"David","family":"Aldous","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"Asymptotic fringe distributions for general famileis of random trees","author":"Aldous D. J.","journal-title":"Ann. Appl. Probab."},{"key":"e_1_2_1_3_2","article-title":"The continuum random tree I","author":"Aldous D. J.","journal-title":"Ann. Probab."},{"key":"e_1_2_1_4_2","unstructured":"F.AvramandD.Bertsimas The Minimum Spanning Tree Constant in Geometric Probability and under the Independent Model: A Unified Approach Tech. Rep. Massachusetts Institute of Technology 1990."},{"key":"e_1_2_1_5_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"B.Bollob\u00e1sandI.Simon On the expected behavior of disjoint set union algorithms in Proc. 17th STOC 1985 pp.224\u2013231.","DOI":"10.1145\/22145.22171"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(85)90058-7"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(78)90009-9"},{"key":"e_1_2_1_9_2","first-page":"361","article-title":"On finding the expected length of a random minimal tree","volume":"32","author":"Timofeev E. A.","year":"1987","journal-title":"The Probab. Appl."},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"A.Yao On the average behavior of set merging algorithms in Proc. 8th STOC 1976 pp.192\u2013195.","DOI":"10.1145\/800113.803648"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240010402","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240010402","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:57:12Z","timestamp":1698001032000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240010402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1990,12]]}},"alternative-id":["10.1002\/rsa.3240010402"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240010402","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,12]]}}}