On Hamiltonian decompositions of complete 3-uniform hypergraphs

Based on the definition of Hamiltonian cycles by Katona and Kierstead, we present a recursive construction of tight Hamiltonian decompositions of complete 3-uniform hypergraphs K n ( 3 ), and complete multipartite 3-uniform hypergraph K t ( n ) ( 3 ), where t is the number of partite sets and n is the size of each partite set. For t ≡ 4, 8 ( mod 12 ), we utilize a tight Hamiltonian decomposition of K t ( 3 ) to construct those of K 2 t ( 3 ) and K t ( n ) ( 3 ) for all positive integers n. By applying our method in conjunction with the current results in literature, we obtain tight Hamiltonian decompositions for infinitely many hypergraphs, namely complete hypergraphs K t ( 3 ) and complete multipartite hypergraphs K t ( n ) ( 3 ) for any positive integer n, and t = 2 m, 5 ⋅ 2 m, 7 ⋅ 2 m, and 11 ⋅ 2 m when m ≥ 2.