On the Hamiltonian cycle Decompositions of Complete 3-Uniform Hypergraphs

Abstract

Abstract A 3-uniform hypergraph H is a pair (V,ϵ), where V is vertex set, ϵ, is a family of 3-subsets of V. If ϵ consists of all 3-subsets of V, H is a complete 3-uniform hypergraph on n vertices and is denoted by K n(3). If V is the disjoint union of sets (so-called parts) V1 and V2, and ϵ consists of all possible 3-subsets ζ of V1 ∪ V2 such that ζ ⊈ Vi, i = 1, 2, then H is a complete bipartite 3-uniform hypergraph and is denoted by K m,n(3), if ∣V1∣ = m, ∣V2∣ = n. In this paper we show that following results on the decomposition of hypergraph into Hamiltonian cycles. (i) K n,n(3) has a decomposition into Hamiltonian cycles, n ≥ 2. (ii) all complete 3-uniform hypergraphs K 2m(3) with 2m vertices has a decomposition into Hamiltonian cycles, m ≥ 2.