%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is mydata.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% You and your thesis
\newcommand{\myname}{Benjamin Shemmer}
\newcommand{\mytitle}{On Graphs With a Given Endomorphism Monoid}
\newcommand{\mydegree}{B.A., Wesleyan University, 2001}
\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}{Vojt\v{e}ch R\"{o}dl, Ph.D.}
% other committee members should be in alphabetical order
\newcommand{\committeeone}{Dwight Duffus, Ph.D.}
\newcommand{\committeetwo}{Ron Gould, Ph.D.}

%%% Acknowledgments
\newcommand{\myacknowledgments}{
This work would not have been possible without the help of a great many people. I would like to thank
my advisor Vojt\v{e}ch R\"{o}dl for his support, wisdom and humor. My collaborator V\'{a}clav Koubek for his
persistence and patience. James Nagy, the director of graduate studies, and Terry Ingram, the department secretary, for doing their jobs
well and honorably. Professors Ron Gould and Dwight Duffus for teaching me well and being on my thesis committee. Professor Aaron Abrams for generously sharing his knowledge and providing invaluable counsel.}

%%% Abstract
\newcommand{\myabstract}{
Hedrl\'\i n and Pultr proved that for any monoid $\mathbf{M}$
there exists a graph $G$ with endomorphism monoid isomorphic to
$\mathbf{M}$. We will give a construction $G(\mathbf{M})$
for a graph with prescribed endomorphism monoid $\mathbf{M}$.
Using this construction we derive bounds on the minimum number of
vertices and edges required to produce a graph with a given
endomorphism monoid for various classes of finite monoids. We
state bounds for the class of all monoids as well as for certain
subclasses -- groups, k-cancellative monoids, commutative
3-nilpotent monoids, rectangular groups,completely simple
monoids, a variety of strong semillatices and others.
}


%%% Dedication
\newcommand{\mydedication}{
For my brother, my keeper, Yadin.
}