Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles

[摘要] It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order \(v\) if and only if \(v \equiv 0, 1,\text{ or }2\ (\operatorname{mod} 9)\). For all positive integers \(\lambda\) and \(v\), we find a maximum packing with loose 3-cycles of the \(\lambda\)-fold complete 3-uniform hypergraph of order \(v\). We show that, if \(v \geq 6\), such a packing has a leave of two or fewer edges.

[学科分类] 环境科学（综合）

[关键词] maximum packing;\(\lambda\)-fold complete 3-uniform hypergraph;loose 3-cycle.