Physical Sciences and Mathematics Commons^™

Embedding Factorizations, Anna Johnsen

Theses and Dissertations

Let $V$ be a set of $n$ vertices for some $n\in\mathbb{N}$ and let $E$ be a collection of $h$-subsets of $V$. Then $\mathscr G = (V,E)$ is an $h$-unifrom hypergraph and we refer to $V$ as its vertex set and to $E$ as its edge set. We say that $\mathscr G$ is complete and denote it by $K_n^h$ if every $h$-subset of $V$ is contained in $E$. If every edge in $E$ is repeated $\lambda$ times, we say $G$ is $\lambda$-fold. Specifically, $\lambda K_n^h$ is the complete $\lambda$-fold $n$-vertex $h$-uniform hypergraph with an edge set containing $\lambda$ copies of every …