Decomposing the complete r-graph.

Let f r ( n ) be the minimum number of complete r -partite r -graphs needed to partition the edge set of the complete r -uniform hypergraph on n vertices. Graham and Pollak showed that f 2 ( n ) = n − 1 . An easy construction shows that f r ( n ) ≤ ( 1 − o ( 1 ) ) ( n ⌊ r / 2 ⌋ ) and it has been unknown if this upper bound is asymptotically sharp. In this paper we show that f r ( n ) ≤ ( 14 15 + o ( 1 ) ) ( n r / 2 ) for each even r ≥ 4 . [ABSTRACT FROM AUTHOR]