Abstract : A crucial lemma in recent work of the author (showing that k-term arithmetic progression-free sets of integers must have density zero) stated (approximately) that any large bipartite graph… Expand

In 1926 van der Waerden [13] proved the following startling theorem : If the set of integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily long arithmetic… Expand

We define a perfect matching in a k-uniform hypergraph H on n vertices as a set of @?n/k@? disjoint edges. Let @d"k"-"1(H) be the largest integer d such that every (k-1)-element set of vertices of H… Expand

We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time.Expand