5 problems

Let $K_m^h$ and $K_n^h$ be complete $h$-uniform hypergraphs on $m$ and $n$ vertices, respectively, where $n>m$. A 1-factorization is an edge-coloring whose color classes are $1$-re…

A partial $6$-factorization is a collection of edge-disjoint $6$-factors, called colors, in a sub-hypergraph of the complete $3$-uniform hypergraph $K_{10}^3$; an extension is a…

Let $cmathcal{L}$ be a set of distinct positive integers whose largest element is $k$. The non-uniform set system $cbinom{[n]}{cmathcal{L}}$ consists of the subsets of $[n]$ whose…

Let $\mathscr K_{m_1,\ldots,m_n}^{3}$ be the complete multipartite 3-uniform hypergraph whose parts have sizes $m_1,\ldots,m_n$, and let $\lambda \mathscr K_{m_1,\ldots,m_n}^{3}$ d…

Let $K_n^h$ be the complete $h$-uniform hypergraph on $n$ vertices. A 1-factor is a spanning 1-regular sub-hypergraph, and $K_n^h$ is 1-factorable when its edge set can be partitio…