 
Summary: The de BruijnErdos Theorem for
Hypergraphs
Noga Alon
Keith E. Mellinger
Dhruv Mubayi
Jacques Verstrašete §
July 23, 2010
Abstract
Fix integers n r 2. A clique partition of [n]
r is a collection of proper subsets
A1, A2, . . . , At [n] such that i
Ai
r is a partition of [n]
r .
Let cp(n, r) denote the minimum size of a clique partition of [n]
r . A classical theorem of
de Bruijn and Erdos states that cp(n, 2) = n. In this paper we study cp(n, r), and show in
general that for each fixed r 3,
cp(n, r) (1 + o(1))nr/2
as n .
