On Partitioning and Packing Products with Rectangles

In [1] we introduced and studied for product hypergraphs Hn = Qni=1Hi , where Hi = (Vi; Ei) , the minimal size (Hn) of a partition of Vn =Qni=1 Vi into sets that are elements of En = Qni=1 Ei . The main result was that (Hn) = n Y i=1 (Hi); (1) if the Hi's are graphs with all loops included. A key step in the proof concerns the special case of complete graphs. Here we show that (1) also holds when the Hi are complete d{uniform hypergraphs with all loops included, subject to a condition on the sizes of the Vi . We present also an upper bound on packing numbers.