On Decompositions of Complete 3-Uniform Hypergraphs into a Linear Forest with 4 Edges
摘要
A 3-uniform linear forest is any hypergraph obtained by starting with a single 3-uniform edge and adding other 3-uniform edges sequentially such that each additional edge intersects with the previous hypergraph at no more than one vertex. There are nine such 3-uniform linear forests with four edges. In this paper we establish necessary and sufficient conditions for a decomposition of a complete 3-uniform hypergraph into isomorphic copies of a linear forest with four edges.