Dependent random choice
نویسندگان
چکیده
We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss some of them.
منابع مشابه
6 - Dependent Random Choice
If F is a family of graphs containing a bipartite graph, then for some δ > 0, ex(n,F) < n2−δ by the Kövari-Sós-Turán Theorem. Erdős and Simonovits [5] conjectured that for every finite family graph F of graphs, there exists α = α(F) such that ex(n,F) = Θ(nα). This α is called the exponent of F . If F is a bipartite graph containing a cycle, then in general it is not known if F = {F} has an expo...
متن کاملThe Comparison of the Effects of Choice Theory Therapy and Behavioral Activation Therapy with and without Guided Mental Imagery on Resilience in Substance-Dependent Adolescents
Objective: This study aimed to compare the effects of choice theory therapy and behavioral activation (BA) therapy with and without guided mental imagery on resilience in substance-dependent adolescents. Method: The present study was quasi-experimental with pretest-posttest design with a control group. The study sample included 60 substance-dependent adolescents who were selected by convenience...
متن کاملThe Effectiveness of Group Reality Therapy Based on Choice Theory on Responsibility, Locus of Control, and Dose Reduction of Agonist Drugs in Substance-Dependent Individuals under Maintenance Treatment
Objective: The present research aimed to evaluate the effectiveness of group reality therapy based on choice theory on responsibility, locus of control, and dose reduction of agonist drugs in substance-dependent individuals under maintenance treatment. Method: The research method was quasi-experimental with a pre-test, post-test, and follow-up design with a control group. The statistical popula...
متن کاملمقایسه زمان واکنش در افراد وابسته به مواد و افراد غیروابسته
Aim: The aim of this study was to compare the simple, selective, and discrimination reaction time in substance-dependent and non-dependent individuals. Method: In this causal-comparative study, the population included of 425 males (opium and crystal dependents) who were referred to addiction rehabilitation centers in Tabriz. By random sampling, 16 opium dependents, 16 crystal dependents, and 16...
متن کاملStrong Convergence of Weighted Sums for Negatively Orthant Dependent Random Variables
We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.
متن کاملSome Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Random Struct. Algorithms
دوره 38 شماره
صفحات -
تاریخ انتشار 2011