{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T12:41:35Z","timestamp":1698151295972},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2007,7,5]],"date-time":"2007-07-05T00:00:00Z","timestamp":1183593600000},"content-version":"vor","delay-in-days":5970,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1991,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The \u201cbest\u201d inequalities of type P{(\u03b6, \u03b7)\u2282 <jats:italic>E}<\/jats:italic> \u2267<jats:italic>f<\/jats:italic>(P{\u03b7\u2282 <jats:italic>D<\/jats:italic><jats:sub>1<\/jats:sub>}P{\u03b7\u2282D<jats:italic>m<\/jats:italic>}) for independent and identically distributed random elements \u03b6 and \u03b7 can be reduced to Tur\u00e1n\u2010type problems for graphs with colored vertices. In the present work we describe a finite algorithm for obtaining the asymptotical solution for an arbitrary problem of such type. In the case of two colors we obtain the final form of asymptotic solution without using the algorithm.<\/jats:p>","DOI":"10.1002\/rsa.3240020107","type":"journal-article","created":{"date-parts":[[2010,7,12]],"date-time":"2010-07-12T08:12:25Z","timestamp":1278922345000},"page":"73-99","source":"Crossref","is-referenced-by-count":1,"title":["Inequalities in probability theory and tur\u00e1n\u2010type problems for graphs with colored vertices"],"prefix":"10.1002","volume":"2","author":[{"given":"A. F.","family":"Sidorenko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,7,5]]},"reference":[{"key":"e_1_2_1_1_2","volume-title":"Extremal Graph Theory","author":"Bollob\u00f3s B.","year":"1978"},{"key":"e_1_2_1_2_2","first-page":"343","article-title":"Complete subgraphs of chromatic graphs and hypergraphs","volume":"6","author":"Bollob\u00e1s B.","year":"1974","journal-title":"Utilitas Math."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90034-8"},{"key":"e_1_2_1_4_2","first-page":"119","article-title":"Inverse extremal digraph problems, Finite and Infinite Sets, Eger (Hungary)","volume":"37","author":"Brown W. G.","year":"1981","journal-title":"Colloq. Math. Soc. 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F.","year":"1989","journal-title":"Discrete Math."},{"key":"e_1_2_1_18_2","first-page":"999","volume-title":"Combinatorial Theory and Its Applications","author":"Simonovits M.","year":"1970"},{"key":"e_1_2_1_19_2","first-page":"161","volume-title":"Selected Topics in Graph Theory, 2","author":"Simonovits M.","year":"1983"},{"key":"e_1_2_1_20_2","first-page":"436","article-title":"Egy gr\u00e1felm\u00e9leti sz\u00e9ls\u00f6\u00e9rt\u00e9kfeladatr\u00f3l","volume":"48","author":"Tur\u00e1n P.","year":"1941","journal-title":"Mat. \u00e9s Fiz. 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