Theses and Dissertations Collection

In this dissertation, we discuss cycles of length at least six. We prove that (Theorem 1) if $G$ is a graph of order $n\geq 6k+1$ and the minimum degree of $G$ is at least $\displaystyle\frac{7k}{2}$, then $G$ contains $k$ disjoint cycles of length at least six, and (Theorem 2) if $G$ is a graph of order $n\geq 6k+6$ and the minimum degree of $G$ is at least $\displaystyle\frac{n}{2}$, then $G$ contains $k$ disjoint cycles covering all the vertices of $G$ such that $k-1$ are 6-cycles.