{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:28:01Z","timestamp":1774369681128,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":9437,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1980,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The number of connected graphs on <jats:italic>n<\/jats:italic> labeled points and <jats:italic>q<\/jats:italic> lines (no loops, no multiple lines) is <jats:italic>f(n,q).<\/jats:italic> In the first paper of this series I showed how to find an (increasingly complicated) exact formula for <jats:italic>f(n,n+k)<\/jats:italic> for general <jats:italic>n<\/jats:italic> and successive <jats:italic>k.<\/jats:italic> The method would give an asymptotic approximation to <jats:italic>f(n,n+k)<\/jats:italic> for any fixed <jats:italic>k<\/jats:italic> as <jats:italic>n<\/jats:italic> \u2192 \u221e. Here I find this approximation when <jats:italic>k<\/jats:italic> = <jats:italic>o(n<\/jats:italic><jats:sup>1\/3<\/jats:sup>), a much more difficult matter. The problem of finding an approximation to <jats:italic>f(n,q)<\/jats:italic> when <jats:italic>q<\/jats:italic> &gt; <jats:italic>n<\/jats:italic> + <jats:italic>Cn<\/jats:italic><jats:sup>1\/3<\/jats:sup> and (2 <jats:italic>q\/n<\/jats:italic>) \u2010 log <jats:italic>n<\/jats:italic> \u2192 \u2010 \u221e is open.<\/jats:p>","DOI":"10.1002\/jgt.3190040409","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:30:16Z","timestamp":1180420216000},"page":"393-407","source":"Crossref","is-referenced-by-count":50,"title":["The number of connected sparsely edged graphs. III. Asymptotic results"],"prefix":"10.1002","volume":"4","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","first-page":"3","article-title":"Random graphs with degree of connectedness 2","volume":"22","author":"Bagaev G. N.","year":"1973","journal-title":"Diskret. Analiz"},{"key":"e_1_2_1_3_2","first-page":"376","article-title":"A theorem on trees","volume":"23","author":"Cayley A.","year":"1889","journal-title":"Quart. J. Math."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"290","DOI":"10.5486\/PMD.1959.6.3-4.12","article-title":"On random graphs. I","volume":"6","author":"Erd\u00f6s P.","year":"1959","journal-title":"J. Publ. Math. Debrecen"},{"key":"e_1_2_1_5_2","first-page":"17","article-title":"On the evolution of random graphs","volume":"5","author":"Erd\u00f6s P.","year":"1960","journal-title":"Magyar Tud. Akad. Mat. Kut. Int. K\u00f6zl."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010408"},{"key":"e_1_2_1_7_2","first-page":"385","article-title":"On connected graphs I","volume":"4","author":"R\u00e9nyi A.","year":"1959","journal-title":"Publ. Math. Inst. Hungarian Acad. Sci."},{"key":"e_1_2_1_8_2","first-page":"193","article-title":"Solution of the equation ze z a","volume":"65","author":"Wright E. M.","year":"1959","journal-title":"Proc. Roy. Soc. Edinburgh"},{"key":"e_1_2_1_9_2","first-page":"298","article-title":"Asymptotic enumeration of connected graphs","volume":"68","author":"Wright E. M.","year":"1970","journal-title":"Proc. Roy. Soc. Edinburgh"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010407"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020403"},{"key":"e_1_2_1_12_2","unstructured":"E. M.Wright The number of sparsely edged labelled Hamiltonian graphs. In preparation."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190040409","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190040409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T18:18:23Z","timestamp":1697739503000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190040409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1980,12]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1980,12]]}},"alternative-id":["10.1002\/jgt.3190040409"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190040409","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1980,12]]}}}