• Corpus ID: 119671539

Transference for the Erd\H{o}s-Ko-Rado theorem

@article{Balogh2016TransferenceFT,
  title={Transference for the Erd\H\{o\}s-Ko-Rado theorem},
  author={J{\'o}zsef Balogh and B'ela Bollob'as and Bhargav P. Narayanan},
  journal={arXiv: Combinatorics},
  year={2016}
}
For natural numbers $n,r \in \mathbb{N}$ with $n\ge r$, the Kneser graph $K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\dots,n\}$ in which two sets are adjacent if and only if they are disjoint. Delete the edges of $K(n,r)$ with some probability, independently of each other: is the independence number of this random graph equal to the independence number of the Kneser graph itself? We answer this question affirmatively as long as $r/n$ is bounded away from $1/2$, even when… 
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References

SHOWING 1-10 OF 27 REFERENCES

Combinatorial theorems in sparse random sets

We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\'an's theorem, Szemer\'edi's theorem and Ramsey's theorem, hold almost

Intersecting Families are Essentially Contained in Juntas

It is proved that every intersecting family of k-sets is almost contained in a dictatorship, a 1-junta (which by the Erdős–Ko–Rado theorem is a maximal intersectingfamily), and the methods combine traditional combinatorics with results stemming from the theory of Boolean functions and discrete Fourier analysis.

Hypergraph containers

We develop a notion of containment for independent sets in hypergraphs. For every $$r$$r-uniform hypergraph $$G$$G, we find a relatively small collection $${\mathcal C}$$C of vertex subsets, such

Threshold functions for Ramsey properties

. Probabilistic methods have been used to approach many problems of Ramsey theory. In this paper we study Ramsey type questions from the point of view of random structures. Let K(n, N) be the random

Arithmetic progressions of length three in subsets of a random set

0. Introduction. In 1936 Erdős and Turan [ET 36] asked whether for every natural number k and every positive constant α, every subset A of [n] = {0, 1, . . . , n − 1} with at least αn elements

On the measure of intersecting families, uniqueness and stability

It is proved, for a certain range of parameters, that the t-intersecting families of maximal measure are the families of all sets containing t fixed elements, and that the extremal examples are not only unique, but also stable.

INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set

The typical structure of intersecting families of discrete structures

The study of intersecting structures is central to extremal combinatorics. A family of permutations F ⊂ Sn is t-intersecting if any two permutations in F agree on some t indices, and is trivial if

On independent sets in hypergraphs

It is proved that if Hn is an n-vertex r+1-uniform hypergraph in which every r-element set is contained in at most d edges, where 0 0 satisfies cr~r/e as ri¾?∞, then cr improves and generalizes several earlier results and gives an application to hypergraph Ramsey numbers involving independent neighborhoods.