{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T17:49:16Z","timestamp":1781891356655,"version":"3.54.5"},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7886,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A spanning subgraph <jats:italic>H<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is called a <jats:italic>K<\/jats:italic><jats:sub><jats:italic>l<\/jats:italic><\/jats:sub>\u2010factor if each component of <jats:italic>H<\/jats:italic> is isomorphic to the complete graph of order <jats:italic>l.<\/jats:italic> We determine the minimum size for any graph to have a <jats:italic>K<\/jats:italic><jats:sub><jats:italic>l<\/jats:italic><\/jats:sub>\u2010factor. Relating this result, we give a new short proof of the Erd\u00f6s\u2010Gallai theorem on the maximum size of graphs with at most \u03b2 independent edges.<\/jats:p>","DOI":"10.1002\/jgt.3190090117","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:19:10Z","timestamp":1180423150000},"page":"197-201","source":"Crossref","is-referenced-by-count":25,"title":["On the size of graphs with complete\u2010factors"],"prefix":"10.1002","volume":"9","author":[{"given":"Jin","family":"Akiyama","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Frankl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Digraphs","author":"Behzad M.","year":"1979"},{"key":"e_1_2_1_3_2","first-page":"181","article-title":"On the minimal number of vertices representing the edges of a graph","volume":"6","author":"Erdos P.","year":"1961","journal-title":"Publ. Math. Inst. Hungar. Acad. Sci."},{"key":"e_1_2_1_4_2","series-title":"Colloq. Math. Soc. J. Bolyai 4","first-page":"601","volume-title":"Combinatorial Theory and its Applications","author":"Hajnal A.","year":"1970"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190090117","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T05:45:06Z","timestamp":1697867106000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190090117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1985,3]]}},"alternative-id":["10.1002\/jgt.3190090117"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190090117","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,3]]}}}