{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T11:14:13Z","timestamp":1698146053589},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5331,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For every <jats:italic>r<\/jats:italic>\u2010graph <jats:italic>G<\/jats:italic> let \u03c0(<jats:italic>G<\/jats:italic>) be the minimal real number \u03f5 such that for every \u03f5 &lt; 0 and <jats:italic>n<\/jats:italic> \u03f5 <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>(\u03bb, <jats:italic>G<\/jats:italic>) every <jats:italic>R<\/jats:italic>\u2010graph <jats:italic>H<\/jats:italic> with <jats:italic>n<\/jats:italic> vertices and more than (\u03c0 + \u03f5)(nr) edges contains a copy of <jats:italic>G<\/jats:italic>. The real number \u03bb(<jats:italic>G<\/jats:italic>) is defined in the same way, adding the constraint that all independent sets of vertices in <jats:italic>H<\/jats:italic> have size 0(<jats:italic>n<\/jats:italic>). Erd\u00f6s and S\u00f3s asked whether there exist <jats:italic>r<\/jats:italic>\u2010graphs <jats:italic>G<\/jats:italic> with \u03c0(<jats:italic>G<\/jats:italic>) &lt; \u03bb(<jats:italic>G<\/jats:italic>) &lt; 0. Frankl and R\u00f6dl proved that there exist infinitely many such <jats:italic>r<\/jats:italic>\u2010graphs for every <jats:italic>r<\/jats:italic> \u2266 3. However, no example of an <jats:italic>r<\/jats:italic>\u2010graph with above property was known. We construct an example of such a 3\u2010graph with 7 vertices and 9 edges.<\/jats:p>","DOI":"10.1002\/jgt.3190160108","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T01:49:33Z","timestamp":1181267373000},"page":"73-78","source":"Crossref","is-referenced-by-count":1,"title":["On ramsey\u2010tu\u0155an numbers for 3\u2010graphs"],"prefix":"10.1002","volume":"16","author":[{"given":"A. F.","family":"Sidorenko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90105-8"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(76)90057-5"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02020444"},{"key":"e_1_2_1_5_2","first-page":"51","article-title":"A limit theorem in graph theory","volume":"1","author":"Erd\u00f6s P.","year":"1966","journal-title":"Stud. Sci. Math. Hung."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579235"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579342"},{"key":"e_1_2_1_8_2","first-page":"395","article-title":"Some remarks on Ramsey's and Tur\u00e1n's theorem","volume":"4","author":"Erd\u00f6s P.","year":"1969","journal-title":"Comb. Theory Appl. Math. 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