{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T16:02:27Z","timestamp":1762272147793},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2017,8,14]],"date-time":"2017-08-14T00:00:00Z","timestamp":1502668800000},"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":[[2018,7]]},"abstract":"<jats:p>We consider the problem of minimizing the number of edges that are contained in triangles, among <jats:italic>n<\/jats:italic>-vertex graphs with a given number of edges. For sufficiently large <jats:italic>n<\/jats:italic>, we prove an exact formula for this minimum, which partially resolves a conjecture of F\u00fcredi and Maleki.<\/jats:p>","DOI":"10.1017\/s0963548317000189","type":"journal-article","created":{"date-parts":[[2017,8,13]],"date-time":"2017-08-13T22:29:38Z","timestamp":1502663378000},"page":"580-622","source":"Crossref","is-referenced-by-count":3,"title":["Minimizing the Number of Triangular Edges"],"prefix":"10.1017","volume":"27","author":[{"given":"VYTAUTAS","family":"GRUSLYS","sequence":"first","affiliation":[]},{"given":"SHOHAM","family":"LETZTER","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,8,14]]},"reference":[{"key":"S0963548317000189_ref5","unstructured":"F\u00fcredi Z. and Maleki Z. A proof and a counterexample for a conjecture of Erd\u0151s concerning the minimum number of edges on odd cycles. Manuscript."},{"key":"S0963548317000189_ref10","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1965-053-6"},{"key":"S0963548317000189_ref11","unstructured":"Rademacher H. (1941). Unpublished manuscript."},{"key":"S0963548317000189_ref1","first-page":"13","article-title":"Some theorems on graphs (in Hebrew).","volume":"9","author":"Erd\u0151s","year":"1955","journal-title":"Riveon Lematematika"},{"key":"S0963548317000189_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009085"},{"key":"S0963548317000189_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548316000407"},{"key":"S0963548317000189_ref6","unstructured":"Grzesik A. , Hu P. and Volec J. Minimum number of edges that occur in odd cycles. arXiv:1605.09055"},{"key":"S0963548317000189_ref7","first-page":"431","volume-title":"Proc. Fifth British Combinatorial Conference (Aberdeen 1975)","author":"Lov\u00e1sz","year":"1976"},{"key":"S0963548317000189_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5438-2_41"},{"key":"S0963548317000189_ref13","first-page":"436","article-title":"Eine Extremalaufgabe aus der Graphentheorie.","volume":"48","author":"Tur\u00e1n","year":"1941","journal-title":"Mat. Fiz Lapok"},{"key":"S0963548317000189_ref2","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1215\/ijm\/1255631811","article-title":"On a theorem of Rademacher\u2013Tur\u00e1n.","volume":"6","author":"Erd\u0151s","year":"1962","journal-title":"Illinois J. Math"},{"key":"S0963548317000189_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(92)90586-5"},{"key":"S0963548317000189_ref9","first-page":"60","article-title":"Problem 28.","volume":"10","author":"Mantel","year":"1907","journal-title":"Wiskundige Opgaven"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548317000189","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,14]],"date-time":"2019-04-14T15:06:41Z","timestamp":1555254401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548317000189\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,14]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["S0963548317000189"],"URL":"https:\/\/doi.org\/10.1017\/s0963548317000189","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,14]]}}}