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Inequalities in probability theory and turán‐type problems for graphs with colored vertices
Author(s) -
Sidorenko A. F.
Publication year - 1991
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.3240020107
Subject(s) - colored , mathematics , type (biology) , independent and identically distributed random variables , combinatorics , random graph , inequality , discrete mathematics , random variable , graph , statistics , mathematical analysis , ecology , materials science , composite material , biology
The “best” inequalities of type P{(ζ, η)⊂ E} ≧ f (P{η⊂ D 1 }P{η⊂D m }) for independent and identically distributed random elements ζ and η can be reduced to Turán‐type 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.