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{\bf \noindent Distribution Agreement}

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\noindent In presenting this thesis or dissertation as a partial fulfillment of the requirements for an advanced degree from Emory University, I hereby grant to Emory University and its agents the non-exclusive license to archive, make accessible, and display my thesis or dissertation in whole or in part in all forms of media, now or hereafter known, including display on the world wide web. I understand that I may select some access restrictions as part of the online submission of this thesis or dissertation. I retain all ownership rights to the copyright of the thesis or dissertation. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.

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Signature:
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Megan Cream\end{tabular}

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On Chorded Cycles

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By

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Megan Cream \\
Doctor of Philosophy

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Mathematics

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Ron Gould\\
Advisor

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Dwight Duffus \\
Committee Member

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Vojtech Rodl\\
Committee Member

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Accepted:

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Lisa A. Tedesco, Ph.D. \\
Dean of the James T. Laney School of Graduate Studies 

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Date
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On Chorded Cycles

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By

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Megan Cream \\

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Advisor: Ron Gould, Ph.D.

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An abstract of \\
A dissertation submitted to the Faculty of the \\
James T. Laney School of Graduate Studies of Emory University \\
in partial fulfillment of the requirements for the degree of \\
Doctor of Philosophy \\
in Mathematics \\
2015

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Abstract 

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On Chorded Cycles\\
By Megan Cream
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\noindent Historically, there have been many results concerning sufficient conditions for implying certain sets of cycles in graphs.  My thesis aims to extend many of these well known results to similar results on sets of {\it chorded} (and sometimes even {\it doubly chorded}) cycles.  In particular, we consider the minimum degree, $\delta(G)$ and a Ore-type degree sum condition, $\sigma_2(G)$ of a graph $G$, sufficient to guarantee the existence of $k$ vertex disjoint chorded cycles, often containing specified elements of the graph, such as certain vertices or edges.  Further, we extend a result on vertex disjoint cycles and chorded cycles to an analogous result on vertex disjoint cycles and {\it doubly} chorded cycles. We define a new graph property called chorded pancyclicity, and investigate a density condition and forbidden subgraphs in claw-free graphs that imply this new property. Specifically, we forbid certain paths and triangles with pendant paths.  This is joint work with Dongqin Cheng, Ralph Faudree, Ron Gould, and Kazuhide Hirohata.

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On Chorded Cycles

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By

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Megan Cream \\

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Advisor: Ron Gould, Ph.D.

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A dissertation submitted to the Faculty of the \\
James T. Laney School of Graduate Studies of Emory University \\
in partial fulfillment of the requirements for the degree of \\
Doctor of Philosophy \\
in Mathematics \\
2014

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