{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T13:39:18Z","timestamp":1772372358135,"version":"3.50.1"},"reference-count":9,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8890,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper concerns the degree sequence <jats:italic>d<\/jats:italic><jats:sub>1<\/jats:sub> \u2265 <jats:italic>d<\/jats:italic><jats:sub>2<\/jats:sub> \u2265 \u2026 \u2265 <jats:italic>d<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> of a randomly labeled graph of order <jats:italic>n<\/jats:italic> in which the probability of an edge is <jats:italic>p(n)<\/jats:italic> \u2266 1\/2. Among other results the following questions are answered. What are the values of <jats:italic>p(n<\/jats:italic>) for which <jats:italic>d<\/jats:italic><jats:sub>1<\/jats:sub>, the maximum degree, is the same for almost every graph? For what values of <jats:italic>p(n<\/jats:italic>) is it true that <jats:italic>d<\/jats:italic><jats:sub>2<\/jats:sub> &gt; <jats:italic>d<\/jats:italic><jats:sub>2<\/jats:sub> for almost every graph, that is, there is a unique vertex of maximum degree? The answers are (essentially) <jats:italic>p(n<\/jats:italic>) = o(<jats:italic>logn\/n\/n<\/jats:italic>) and <jats:italic>p(n)n\/logn<\/jats:italic> \u2192 \u221e. Also included is a detailed study of the distribution of degrees when 0 &lt; lim <jats:italic>n p(n)\/log n<\/jats:italic> \u2266 <jats:styled-content>lim<\/jats:styled-content> <jats:italic>n p(n)\/log n<\/jats:italic> &lt; \u221e.<\/jats:p>","DOI":"10.1002\/jgt.3190060209","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:47:28Z","timestamp":1180421248000},"page":"147-155","source":"Crossref","is-referenced-by-count":31,"title":["Vertices of given degree in a random graph"],"prefix":"10.1002","volume":"6","author":[{"given":"B\u00e9la","family":"Bollob\u00e1s","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Extremal Graph Theory","author":"Bollob\u00e1s B.","year":"1978"},{"key":"e_1_2_1_3_2","volume-title":"Graduate Texts in Math","author":"Bollob\u00e1s B.","year":"1979"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90253-3"},{"key":"e_1_2_1_5_2","volume-title":"A Course in Probability Theory","author":"Chung K. L.","year":"1974"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-2196-8"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.5486\/PMD.1959.6.3-4.12"},{"key":"e_1_2_1_8_2","first-page":"17","article-title":"On the evolution of random graphs","volume":"5","author":"Erd\u00f3s P.","year":"1960","journal-title":"Publ. Math. Inst. Hungar. Acad. Sci."},{"key":"e_1_2_1_9_2","volume-title":"Probabilistic Methods in Combinatorics","author":"Erd\u00f6s P.","year":"1974"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(77)90039-9"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060209","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:22:12Z","timestamp":1699766532000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["10.1002\/jgt.3190060209"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060209","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}