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% This is mydata.tex
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% You and your thesis
\newcommand{\myname}{Silke Gehrke}
\newcommand{\mytitle}{Hamiltonicity and Pancyclicity of $4$-connected, Claw- and Net-free Graphs}
\newcommand{\mydegree}{Master of Science, Emory University, 2008}
\newcommand{\thisyear}{2009}
\newcommand{\mydepartment}{Mathematics}
%%% Can be 'Master of Science' or 'Doctor of Philosophy'
\newcommand{\thisdegree}{Doctor of Philosophy}
%%% type of thesis, can be 'thesis' or 'dissertation'
\newcommand{\typeofthesis}{dissertation}
% Your committee
\newcommand{\myadvisor}{Ronald J. Gould, Ph.D.}
% other committee members should be in alphabetical order
\newcommand{\committeeone}{Dwight Duffus, Ph.D.}
\newcommand{\committeetwo}{Robert Roth, Ph.D.}

%%% Acknowledgments
\newcommand{\myacknowledgments}{
I would like to thank my advisor, Ronald J. Gould, for his support and patience throughout the process. Thanks to his guidance I was able to finish this dissertation in a timely manner. I would also like to thank my committee, Dwight Duffus and Robert Roth for their careful reading and valuable comments. 

Furthermore, I would like to thank my collaborators Michael Ferrara, Colton Magnant and Jeffrey Powell.

Moreover, I would like to thank the entire faculty at Emory for the mathematics they have taught me and for being very helpful and supportive. I am also grateful to the faculty at Technical University in Berlin. Especially, I would like to give   thanks to people that invented and continued the exchange program with the Technical University in Berlin and made it possible for me to study at Emory University. In particular, I would like to thank James G. Nagy, Ronald J. Gould, Vladimir Oliker, 
 and Vaidy Sunderam from Emory University and Udo Simon and 
Alexander I. Bobenko from the Technical University Berlin. 
Of course I must also thank the staff and the graduate students at Emory for their support and for providing a positive work atmosphere. 
I am especially grateful  to Annika Poerschke and Nader Razouk for   supporting me throughout the years and the special support in the beginning.  

Finally, I would like to thank my family and friends for the years of support and encouragement. I would like to give special thanks to my sister, Nicole Gehrke, for inspiring me to do a PhD, and  to my mother, grandmother and  Sabine Schiebert for supporting me and  all my decisions along the way.



%First and foremost, I would like to thank my advisor, Skip Garibaldi, for his continuous support throughout this process. I could not have asked for a better advisor. His encouragement and guidance have meant a great deal to me. I would also like to thank my committee, Eric Brussel \& Parimala, and Vicki Powers and the algebra group at Emory. I have learned a lot from them and have had a lot of fun. And a special thanks to Jodi Black, who was brave enough to share an office with me. I will always have wonderful memories of this group. All of the faculty at Emory have been extremely supportive, and I would especially like to thank Jim Nagy, Ron Gould, and Emily Hamilton for their advice and encouragement. And of course I must thank the staff Erin Nagle, Tiffany Doberstein, Terry Ingram, and Jeri Sandlin, for all of their administrative and moral support.

%Throughout my mathematical career, I have had the privilege of many great mentors and teachers, without whom this Ph.D. may not have happened. I would especially like to thank Murray Siegel and the Summer Honors Program who sparked my mathematical curiosity and Larry Lum, the best high school calculus teacher ever. I am also extremely grateful to the Agnes Scott College mathematics faculty - Larry Riddle, Myrtle Lewin, Bob Leslie, and especially Alan Koch, who introduced me to the wonders of algebra. Julia Garibaldi and Ulrica Wilson provided some of the best advice on getting through a Ph.D. program. I am forever grateful for all of this support.

%Finally, I would like to thank my family for their years of encouragement, and especially I would like to thank my husband, Mark, for his endless support. I wouldn't have made it without him!
}

%%% Abstract
\newcommand{\myabstract}{
A well-known conjecture by Manton Matthews and David Sumner states 
that every $4$-connected $K_{1,3}$ -free graph is hamiltonian. The conjecture itself is still 
wide open, but several special cases have been shown so far.  We will show  results that support that conjecture. Especially, we will show   that if a graph is $4$-connected and 
$\{K_{1,3}$, $N\}$- 
free, where $N =$ $N(i, j, k)$, with $i + j + k = 5$ and $i$, $j$, $k \geq 0$, the graph is 
pancyclic.
}

% If you want this, uncomment the lines at the end of preamble.tex as well
%%% Dedication
\newcommand{\mydedication}{
%Dedication goes here.
To my family,

}