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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.more » « less
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A $k$-factorization of the complete $t$-uniform hypergraph $K^{(t)}_{v}$ is an $H$-decomposition of $K^{(t)}_{v}$ where $H$ is a $k$-regular spanning subhypergraph of $K^{(t)}_{v}$. We use nauty to generate the 2-regular and 3-regular spanning subhypergraphs of $K^{(3)}_v$ for $v\leq 9$ and investigate which of these subhypergraphs factorize $K^{(3)}_v$ or $K^{(3)}_v-I$, where $I$ is a 1-factor. We settle this question for all but two of these subhypergraphs.more » « less
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null (Ed.)Consider the multigraph obtained by adding a double edge to $K_4-e$. Now, let $D$ be a directed graph obtained by orientating the edges of that multigraph. We establish necessary and sufficient conditions on $n$ for the existence of a $(K^{*}_{n},D)$-design for four such orientations.more » « less
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