{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:05:34Z","timestamp":1758823534281},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5513,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1991,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A conjecture of Dirac states that every simple graph with <jats:italic>n<\/jats:italic> vertices and 3<jats:italic>n<\/jats:italic> \u2212 5 edges must contain a subdivision of <jats:italic>K<\/jats:italic><jats:sub>5<\/jats:sub>. We prove that a topologically minimal counterexample is 5\u2010connected, and that no minor\u2010minimal counterexample contains <jats:italic>K<\/jats:italic><jats:sub>4<\/jats:sub> \u2013 <jats:italic>e<\/jats:italic>. Consequently, Dirac's conjecture holds for all graphs that can be embedded in a surface with Euler characteristic at least \u2212 2.<\/jats:p>","DOI":"10.1002\/jgt.3190150405","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T11:19:51Z","timestamp":1181301591000},"page":"389-406","source":"Crossref","is-referenced-by-count":8,"title":["Do 3<i>n<\/i> \u2212 5 edges force a subdivision of <i>K<\/i><sub>5<\/sub>?"],"prefix":"10.1002","volume":"15","author":[{"given":"Andr\u00e9 E.","family":"K\u00e9zdy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick J.","family":"McGuinness","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"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","doi-asserted-by":"publisher","DOI":"10.1007\/BF01361708"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19600220107"},{"key":"e_1_2_1_5_2","volume-title":"Topological Graph Theory","author":"Gross J. L.","year":"1987"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01350657"},{"key":"e_1_2_1_7_2","first-page":"251","volume-title":"Theory of Graphs","author":"Pelik\u00e1n J.","year":"1968"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19740640109"},{"key":"e_1_2_1_9_2","first-page":"97","article-title":"Paths, circuits, and subdivisions","volume":"3","author":"Thomassen C.","year":"1988","journal-title":"J. Graph Theory"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190150405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190150405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T03:46:44Z","timestamp":1698032804000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190150405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["10.1002\/jgt.3190150405"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190150405","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}