m× n matrix A with entries between say− 1 and 1, and an error parameter ε between 0 and 1,
we find a matrix D (implicitly) which is the sum of simple rank 1 matrices so that the sum of …

We develop a notion of containment for independent sets in hypergraphs. For every r r-
uniform hypergraph GG, we find a relatively small collection\mathcal CC of vertex subsets …

Szemerédi's Regularity Lemma proved to be a very powerful tool in extremal graph theory
with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi …

A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which
every three consecutive vertices form an edge. In this paper we prove an approximate and …

Szemerédi's Regularity Lemma proved to be a powerful tool in the area of extremal graph
theory. Many of its applications are based on its accompanying Counting Lemma: If G is an ℓ …

The problem of characterizing all the testable graph properties is considered by many to be
the most important open problem in the area of property testing. Our main result in this paper …

We prove that for every n-dimensional body K, there is a rectangular parallelepiped B of the
same volume as K, such that the projection of B onto any coordinate subspace is at most as …

In 1918, Heinz Prüfer [120] discovered a fascinating relationship between labelled trees with
n vertices and sequences of length n− 2 made of the elements of the set {1, 2,..., n}. This …

Given a hereditary graph property P let pn be the set of those graphs in P on the vertex set
{l,..., n}. Define the constant Cn by Ipnl= 2Cn G). We show that the limit limn-+ DO Cn always …

A hereditary property of graphs is a class of graphs which is closed under taking induced
subgraphs. For a hereditary property P, let P n denote the set of P graphs on n labelled …