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 Erdős 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, ...
