{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T12:43:55Z","timestamp":1751287435863},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2012,1,26]],"date-time":"2012-01-26T00:00:00Z","timestamp":1327536000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p>Let<jats:italic>k<jats:sub>r<\/jats:sub><\/jats:italic>(<jats:italic>n<\/jats:italic>, \u03b4) be the minimum number of<jats:italic>r<\/jats:italic>-cliques in graphs with<jats:italic>n<\/jats:italic>vertices and minimum degree at least \u03b4. We evaluate<jats:italic>k<jats:sub>r<\/jats:sub><\/jats:italic>(<jats:italic>n<\/jats:italic>, \u03b4) for \u03b4 \u2264 4<jats:italic>n<\/jats:italic>\/5 and some other cases. Moreover, we give a construction which we conjecture to give all extremal graphs (subject to certain conditions on<jats:italic>n<\/jats:italic>, \u03b4 and<jats:italic>r<\/jats:italic>).<\/jats:p>","DOI":"10.1017\/s0963548311000745","type":"journal-article","created":{"date-parts":[[2012,1,26]],"date-time":"2012-01-26T11:01:21Z","timestamp":1327575681000},"page":"457-482","source":"Crossref","is-referenced-by-count":3,"title":["Cliques in Graphs With Bounded Minimum Degree"],"prefix":"10.1017","volume":"21","author":[{"given":"ALLAN","family":"LO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,1,26]]},"reference":[{"key":"S0963548311000745_ref11","first-page":"436","article-title":"Eine Extremalaufgabe aus der Graphentheorie","volume":"48","author":"Tur\u00e1n","year":"1941","journal-title":"Mat. Fiz. Lapok"},{"key":"S0963548311000745_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5438-2_41"},{"key":"S0963548311000745_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100052063"},{"key":"S0963548311000745_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548309009857"},{"key":"S0963548311000745_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190130411"},{"key":"S0963548311000745_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90133-2"},{"key":"S0963548311000745_ref8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2010-05189-X"},{"key":"S0963548311000745_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009085"},{"key":"S0963548311000745_ref9","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1203350785"},{"key":"S0963548311000745_ref6","unstructured":"[6] Lo A. S. L. (2010) Cliques in graphs. PhD thesis, University of Cambridge."},{"key":"S0963548311000745_ref3","doi-asserted-by":"crossref","first-page":"290","DOI":"10.21136\/CPM.1969.108598","article-title":"On the number of complete subgraphs and circuits contained in graphs","volume":"94","author":"Erd\u0151s","year":"1969","journal-title":"\u010casopis P\u011bst. Mat."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000745","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,27]],"date-time":"2021-12-27T01:59:17Z","timestamp":1640570357000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000745\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,26]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,5]]}},"alternative-id":["S0963548311000745"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000745","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,26]]}}}