{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T06:10:36Z","timestamp":1697955036263},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6427,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,3]]},"abstract":"Abstract<\/jats:title>A probabilistic result of Bollob\u00e1s and Catlin concerning the largest integer p<\/jats:italic> so that a subdivision of Kp<\/jats:sub><\/jats:italic> is contained in a random graph is generalized to a result concerning the largest integer p<\/jats:italic> so that a subdivision of Ap<\/jats:sub><\/jats:italic> is contained in a random graph for some sequence A<\/jats:italic>1<\/jats:sub>, A<\/jats:italic>2<\/jats:sub>,\u2026 of graphs such that A<\/jats:italic>i<\/jats:italic>+1<\/jats:sub> contains a subdivision of Ai<\/jats:sub><\/jats:italic>. A similar result is proved for subdivisions with odd paths or cycles. The result is applied to disprove a conjecture of Chartrand, Geller, and Hedetniemi. The maximum number of edges in a graph without a subdivision of Kp<\/jats:sub>, p<\/jats:italic> = 4, 5, with odd paths or cycles is determined.<\/jats:p>","DOI":"10.1002\/jgt.3190130111","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:18:15Z","timestamp":1180181895000},"page":"75-85","source":"Crossref","is-referenced-by-count":2,"title":["Some probabilistic and extremal results on subdivisions and odd subdivisions of graphs"],"prefix":"10.1002","volume":"13","author":[{"given":"Leif","family":"Kj\u00e6r J\u00f8rgensen","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_3_2","volume-title":"Graduate Texts in Mathematics","author":"Bollob\u00e1s B.","year":"1979"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(81)90066-6"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90062-5"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(71)90065-7"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90280-7"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579269"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1946-08715-7"},{"key":"e_1_2_1_10_2","unstructured":"A. M. H.GerardsandA.Schrijver Matrices with the Edmonds\u2013Johnson property. Report no. 85363\u2010OR Institut f\u00fcr \u00d6konometri und Operations Research Rheinische Friedrich\u2010Wilhelm\u2010Universit\u00e4t Bonn."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.26"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070215"},{"key":"e_1_2_1_13_2","first-page":"544","volume-title":"Recent Advances in Graph Theory","author":"Toft B.","year":"1975"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130111","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130111","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T16:52:17Z","timestamp":1697907137000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1989,3]]}},"alternative-id":["10.1002\/jgt.3190130111"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130111","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,3]]}}}