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\textsc{Dissertation}
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\textsc{Defense}
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\textit{Partitions of Graphs Under Distance Constraints}
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Colton Magnant\par
Emory University
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\textbf{Abstract:} \begin{abstract}
Let $t$ be an integer and suppose $G$ is a graph on $n$ vertices.  Given an ordered set of $t$ vertices in $G$ and a set of $t$ distances, we find a sharp degree condition for $G$ to contain a hamiltonian cycle with the $t$ vertices in order with approximately the corresponding prescribed distances between them.  We also show similar results for partitioning the graph into paths between chosen vertices or paritioning into cycles containing chosen vertices.
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Advisor: Ron Gould\\
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Friday, February 29, 2008, 4:00 pm\par
Mathematics and Science Center: W301
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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