Get access

A Construction of Almost Steiner Systems

Authors


Abstract

Let n, k, and t be integers satisfying math formula. A Steiner system with parameters t, k, and n is a k-uniform hypergraph on n vertices in which every set of t distinct vertices is contained in exactly one edge. An outstanding problem in Design Theory is to determine whether a nontrivial Steiner system exists for math formula. In this note we prove that for every math formula and sufficiently large n, there exists an almost Steiner system with parameters t, k, and n; that is, there exists a k-uniform hypergraph on n vertices such that every set of t distinct vertices is covered by either one or two edges.

Ancillary