{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:18:52Z","timestamp":1759335532143},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,7,1]],"date-time":"2008-07-01T00:00:00Z","timestamp":1214870400000},"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":[[2008,7]]},"abstract":"<jats:p>Let the random graph<jats:italic>R<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>be drawn uniformly at random from the set of all simple planar graphs on<jats:italic>n<\/jats:italic>labelled vertices. We see that with high probability the maximum degree of<jats:italic>R<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>is \u0398(ln<jats:italic>n<\/jats:italic>). We consider also the maximum size of a face and the maximum increase in the number of components on deleting a vertex. These results extend to graphs embeddable on any fixed surface.<\/jats:p>","DOI":"10.1017\/s0963548308009097","type":"journal-article","created":{"date-parts":[[2008,5,19]],"date-time":"2008-05-19T13:00:00Z","timestamp":1211202000000},"page":"591-601","source":"Crossref","is-referenced-by-count":18,"title":["On the Maximum Degree of a Random Planar Graph"],"prefix":"10.1017","volume":"17","author":[{"given":"COLIN","family":"McDIARMID","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BRUCE","family":"REED","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,7,1]]},"reference":[{"key":"S0963548308009097_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33700-8_15"},{"key":"S0963548308009097_ref5","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198571278.003.0006"},{"key":"S0963548308009097_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2371086"},{"key":"S0963548308009097_ref11","doi-asserted-by":"crossref","DOI":"10.56021\/9780801866890","volume-title":"Graphs on Surfaces","author":"Mohar","year":"2001"},{"key":"S0963548308009097_ref1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.37236\/1659","article-title":"The number of labeled 2-connected planar graphs","volume":"9","author":"Bender","year":"2002","journal-title":"Electron. J. Combin."},{"key":"S0963548308009097_ref2","unstructured":"[2] Bollob\u00e1s B. (2001) Random Graphs, 2nd edn, Vol. 73 of Cambridge Studies in Advanced Mathematics, Cambridge University Press."},{"key":"S0963548308009097_ref4","unstructured":"[4] Gerke S. , McDiarmid C. , Steger A. and Weissl A. (2005) Random planar graphs with n nodes and a fixed number of edges. In Proc. ACM\u2013SIAM Symposium on Discrete Algorithms (SODA), pp. 999\u20131007."},{"key":"S0963548308009097_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-002-0242-2"},{"key":"S0963548308009097_ref8","unstructured":"[8] McDiarmid C. (2006) Random graphs on surfaces. Preprint 722, November 2006, Centre de Recerca Matem\u00e0tica, Barcelona (http:\/\/www.crm.es\/)"},{"key":"S0963548308009097_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.09.007"},{"key":"S0963548308009097_ref6","unstructured":"[6] Gim\u00e9nez O. and Noy M. (2005) Asymptotic enumeration and limit laws of planar graphs. arXiv: math.CO\/0501269."},{"key":"S0963548308009097_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1999.3006"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548308009097","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T12:10:20Z","timestamp":1684411820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548308009097\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["S0963548308009097"],"URL":"https:\/\/doi.org\/10.1017\/s0963548308009097","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}