{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T03:11:13Z","timestamp":1716347473947},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2011,5,31]],"date-time":"2011-05-31T00:00:00Z","timestamp":1306800000000},"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":[[2011,7]]},"abstract":"<jats:p>We prove that the maximum degree \u0394<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>of a random series-parallel graph with<jats:italic>n<\/jats:italic>vertices satisfies \u0394<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>\/log<jats:italic>n<\/jats:italic>\u2192<jats:italic>c<\/jats:italic>in probability, and<jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000198_char1\" \/><\/jats:private-char>\u0394<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>~<jats:italic>c<\/jats:italic>log<jats:italic>n<\/jats:italic>for a computable constant<jats:italic>c<\/jats:italic>&gt; 0. The same kind of result holds for 2-connected series-parallel graphs, for outerplanar graphs, and for 2-connected outerplanar graphs.<\/jats:p>","DOI":"10.1017\/s0963548311000198","type":"journal-article","created":{"date-parts":[[2011,5,31]],"date-time":"2011-05-31T13:19:47Z","timestamp":1306847987000},"page":"529-570","source":"Crossref","is-referenced-by-count":7,"title":["The Maximum Degree of Series-Parallel Graphs"],"prefix":"10.1017","volume":"20","author":[{"given":"MICHAEL","family":"DRMOTA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"OMER","family":"GIM\u00c9NEZ","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARC","family":"NOY","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,5,31]]},"reference":[{"key":"S0963548311000198_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2011.04.010"},{"key":"S0963548311000198_ref7","unstructured":"[7] Drmota M. , Gim\u00e9nez O. and Noy M. The maximum degree of planar graphs. Manuscript in preparation."},{"key":"S0963548311000198_ref11","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1515\/crll.1956.196.67","article-title":"A generalisation of Stirling's formula.","volume":"196","author":"Hayman","year":"1956","journal-title":"J. Reine Angew. Math."},{"key":"S0963548311000198_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2007.04.011"},{"key":"S0963548311000198_ref8","doi-asserted-by":"publisher","DOI":"10.1137\/0403019"},{"key":"S0963548311000198_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548309990368"},{"key":"S0963548311000198_ref5","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20290"},{"key":"S0963548311000198_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009097"},{"key":"S0963548311000198_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"},{"key":"S0963548311000198_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1994.1016"},{"key":"S0963548311000198_ref10","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1999.3006"},{"key":"S0963548311000198_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-211-75357-6"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000198","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T04:25:25Z","timestamp":1686111925000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000198\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,31]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["S0963548311000198"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000198","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5,31]]}}}