A Construction for the Decomposition of Hypergraphs.

The decomposition problems of hypergraph have many practical applications, including network communication, information exchange and other fields. It is well known that the complete k-uniform hypergraph on n vertices can be partitioned into disjoint perfect matchings. The solution given by Baranayai is by using a network flow algorithm. This solution is not explicit and its not linear in the number of hyperedges. It is still desirable for applications to have a direct construction of the disjoint matching and if possible with a linear time algorithm in the number of hyperedges in the hypergraph. Such an efficient construction is known for and . In this paper we present an efficient doubling construction for and .