Journal of Combinatorial Theory Series A
A sharp concentration inequality with application
Random Structures & Algorithms
On the concentration of multivariate polynomials with small expectation
Random Structures & Algorithms
New bounds on nearly perfect matchings in hypergraphs: higher codegrees do help
Random Structures & Algorithms
Concentration of non-Lipschitz functions and applications
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Random Structures & Algorithms
Divide and conquer martingales and the number of triangles in a random graph
Random Structures & Algorithms
On equitable Δ-coloring of graphs with low average degree
Theoretical Computer Science - Graph colorings
An Ore-type theorem on equitable coloring
Journal of Combinatorial Theory Series B
Ranged hash functions and the price of churn
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A short proof of the hajnal–szemerédi theorem on equitable colouring
Combinatorics, Probability and Computing
t-Wise independence with local dependencies
Information Processing Letters
Ore-type versions of Brooks' theorem
Journal of Combinatorial Theory Series B
Equitable colorings of Kronecker products of graphs
Discrete Applied Mathematics
Sub-gaussian tails for the number of triangles in g(n, p)
Combinatorics, Probability and Computing
Equitable colorings of Cartesian products of graphs
Discrete Applied Mathematics
Concentration and moment inequalities for polynomials of independent random variables
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Colorful triangle counting and a MapReduce implementation
Information Processing Letters
The missing log in large deviations for triangle counts
Random Structures & Algorithms
Random Structures & Algorithms
A concentration result with application to subgraph count
Random Structures & Algorithms
Tight upper tail bounds for cliques
Random Structures & Algorithms
Equitable coloring of Kronecker products of complete multipartite graphs and complete graphs
Discrete Applied Mathematics
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Let Γ be a finite index set and k ≥ 1 a given integer. Let further S ⊆ [Γ]≤k be an arbitrary family of k element subsets of Γ. Consider a (binomial) random subset Γp of Γ, where p = (pt : i ∈ Γ) and a random variable X counting the elements of S that are contained in this random subset. In this paper we survey techniques of obtaining upper bounds on the upper tail probabilities P(X ≥ λ + t) for t 0. Seven techniques, ranging from Azuma's inequality to the purely combinatorial deletion method, are described, illustrated, and compared against each other for a couple of typical applications. As one application, we obtain essentially optimal bounds for the upper tails for the numbers of subgraphs isomorphic to K4 or C4 in a random graph G(n, p), for certain ranges of p.