{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T14:53:21Z","timestamp":1768748001296,"version":"3.49.0"},"reference-count":6,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4541,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph <jats:italic>G<\/jats:italic> is a (<jats:italic>k, l<\/jats:italic>)\u2010graph if for any subgraph <jats:italic>H<\/jats:italic> of <jats:italic>G<\/jats:italic>, that |<jats:italic>V(H)<\/jats:italic>| \u2267 implies that k(<jats:italic>H<\/jats:italic>) \u2266 <jats:italic>k<\/jats:italic> \u2212 1. An edge\u2010maximal (<jats:italic>k, l<\/jats:italic>\u2010graph <jats:italic>G<\/jats:italic> is one such that for any <jats:italic>e<\/jats:italic> \u03f5 <jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic><jats:sup><jats:italic>c<\/jats:italic><\/jats:sup>), <jats:italic>G<\/jats:italic> + <jats:italic>e<\/jats:italic> is not a (<jats:italic>k, l<\/jats:italic>)\u2010graph. In [F. T. Boesch and J. A. M. McHugh, \u201eAn Edge Extremal Result for Subcohesion,\u201d\ufe01 <jats:italic>Journal of Combinatorial Theory B<\/jats:italic>, vol. 38 (1985), pp. 1\u20137] a class of edge\u2010maximal graphs was found and used to show best possible upper bounds of the size of edge\u2010maximal (<jats:italic>k, l<\/jats:italic>)\u2010graphs. In this paper, we investigate the lower bounds of the size of edge\u2010maximal (<jats:italic>k, l<\/jats:italic>)\u2010graphs. Let <jats:italic>f(n, k, l<\/jats:italic>) denote the minimum size of edge\u2010maximal (<jats:italic>k, l<\/jats:italic>)\u2010graphs of order <jats:italic>n.<\/jats:italic> We shall give a characterization of edge\u2010maximal (<jats:italic>k, l<\/jats:italic>)\u2010graphs. This characterization is used to determine <jats:italic>f(n, k, l<\/jats:italic>) and to characterize the edge\u2010maximal (<jats:italic>k, l<\/jats:italic>)\u2010graphs with minimum sizes, for all <jats:italic>n<\/jats:italic> \u2266 <jats:italic>k<\/jats:italic> + 2 \u2266 5. Thus prior results in [F.T. Boesch and J. A. M. McHugh, op. cit.; H.\u2010J. Lai, \u201eThe Size of Strength\u2010Maximal Graphs,\u201d\ufe01 <jats:italic>Journal of Graph Theory<\/jats:italic>, vol. 14 (1990), pp. 187\u2013197] are extended.<\/jats:p>","DOI":"10.1002\/jgt.3190180303","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T17:09:48Z","timestamp":1181236188000},"page":"227-240","source":"Crossref","is-referenced-by-count":4,"title":["Edge\u2010maximal (<i>k, i<\/i>)\u2010graphs"],"prefix":"10.1002","volume":"18","author":[{"given":"Hong\u2010Jian","family":"Lai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cun\u2010Quan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(85)90087-5"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140207"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01433466"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0122040"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90162-5"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190180303","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190180303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T02:46:39Z","timestamp":1698115599000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190180303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,5]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1994,5]]}},"alternative-id":["10.1002\/jgt.3190180303"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190180303","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,5]]}}}