{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:36:41Z","timestamp":1774370201588,"version":"3.50.1"},"reference-count":10,"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":8525,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1983,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The number of nonseparable graphs on <jats:italic>n<\/jats:italic> labeled points and <jats:italic>q<\/jats:italic> lines is <jats:italic>u(n, q).<\/jats:italic> In the second paper of this series an exact formula for <jats:italic>u(n, n + k)<\/jats:italic> was found for general <jats:italic>n<\/jats:italic> and successive (small) <jats:italic>k.<\/jats:italic> The method would give an asymptotic approximation for fixed <jats:italic>k<\/jats:italic> as <jats:italic>n \u2192 \u221e<\/jats:italic>. Here an asymptotic approximation to <jats:italic>u(n, n + k)<\/jats:italic> is found when <jats:italic>k = O(n<jats:sup>1\/2<\/jats:sup>)<\/jats:italic> and an approximation to log<jats:italic>u(n, n + k)<\/jats:italic> when <jats:italic>k &lt; (1 \u2010 \u03f5)<\/jats:italic>(1\/3 <jats:italic>n<\/jats:italic>)1\/2. The problem of finding an approximation to <jats:italic>u(n, q)<\/jats:italic> when (q \u2010 n)<jats:italic>\/n<\/jats:italic>1\/2 \u2192 + \u2192 and <jats:italic>q\/n<\/jats:italic> \u2010 1\/2 log<jats:italic>n<\/jats:italic> \u2010 1\/2 log log<jats:italic>n<\/jats:italic> \u2192 \u2010 \u221e is open.<\/jats:p>","DOI":"10.1002\/jgt.3190070211","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:05:29Z","timestamp":1180422329000},"page":"219-229","source":"Crossref","is-referenced-by-count":12,"title":["The number of connected sparsely edged graphs. IV large nonseparable graphs"],"prefix":"10.1002","volume":"7","author":[{"given":"E. M.","family":"Wright","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":"Phase Transitions and Critical Phenomena","author":"Domb C.","year":"1974"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02066689"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010408"},{"key":"e_1_2_1_5_2","first-page":"121","volume-title":"Applications of Graph Theory","author":"Temperley H. N. V.","year":"1979"},{"key":"e_1_2_1_6_2","first-page":"119","volume-title":"Studies in Statistical Mechanics","author":"Uhlenbeck G. E.","year":"1962"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010407"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020403"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190040409"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100057510"},{"key":"e_1_2_1_10_3","first-page":"379","volume":"92","year":"1982","journal-title":"Math. Proc. Cambridge Philos. Soc."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190070211","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190070211","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T23:28:10Z","timestamp":1695770890000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190070211"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1983,6]]}},"alternative-id":["10.1002\/jgt.3190070211"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190070211","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,6]]}}}