{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:08:19Z","timestamp":1699834099920},"reference-count":4,"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":10168,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1978,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph <jats:italic>G<\/jats:italic> is called a supercompact graph if <jats:italic>G<\/jats:italic> is the intersection graph of some family \ud835\udcaf of subsets of a set <jats:italic>X<\/jats:italic> such that \ud835\udcaf satisfies the Helly property and for any <jats:italic>x<\/jats:italic>\u2260<jats:italic>y<\/jats:italic> in <jats:italic>X<\/jats:italic>, there exists <jats:italic>S<\/jats:italic> \u2208 \ud835\udcaf with <jats:italic>x<\/jats:italic> \u2208 <jats:italic>S<\/jats:italic>, <jats:italic>y<\/jats:italic> \u2209 <jats:italic>S<\/jats:italic>. Various characterizations of supercompact graphs are given. It is shown that every clique\u2010critical graph is supercompact. Furthermore, for any finite graph, <jats:italic>H<\/jats:italic>, there is at most a finite number of different supercompact graphs <jats:italic>G<\/jats:italic> such that <jats:italic>H<\/jats:italic> is the clique\u2010graph of <jats:italic>G<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/jgt.3190020410","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:17:07Z","timestamp":1180419427000},"page":"349-355","source":"Crossref","is-referenced-by-count":2,"title":["On supercompact graphs"],"prefix":"10.1002","volume":"2","author":[{"given":"Chong\u2010Keang","family":"Lim","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":"29","article-title":"Graph representations of topological spaces","volume":"52","author":"De Groot J.","year":"1974","journal-title":"Math. Centrum Amsterdam"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90084-7"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90109-X"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190020410","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190020410","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T11:00:06Z","timestamp":1699786806000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190020410"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,12]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1978,12]]}},"alternative-id":["10.1002\/jgt.3190020410"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190020410","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,12]]}}}