% SAMPLE ARTICLE FOR COMBINATORIAL THEORY
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\documentclass[12pt]{article}
\usepackage{ct}

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\keywords{Broglington manifolds, permutations}

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\MSC{05C88, 05C89}

% TITLE
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\title{An elementary proof\\ of the reconstruction conjecture}

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\author[1]{First Author\thanks{Supported by NASA grant ABC123.}}
\author[2]{Some Second Author}
\author[3]{Some Third Author}

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\affil[1]{%
% Name of Department, Name of Institution, City and / or State, Country
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School of Hard Knocks, University of Western Nowhere, Somewhere, Australia

% leave a blank line and write the emails in the author's order
\email{ssa@uwn.edu.au}, \email{sta@uwn.edu.au}%
}

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% AUTHORS COMMANDS
% Enter here all commands you need (and no more) in this paper.
% \newcommand{...}{...}

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\begin{document}
%\writedatatofile

\maketitle

% ABSTRACT
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\begin{abstract}
The reconstruction conjecture states that the multiset of
vertex-deleted subgraphs of a graph determines the graph, provided
it has at least 3 vertices. This problem was independently introduced
by Stanis\l aw Ulam (1960) and Paul Kelly (1957). In this paper,
we prove the conjecture by elementary methods.
It is only necessary
to integrate the Lenkle potential of the Broglington manifold over
the quantum supervacillatory measure in order to reduce the set of
possible counterexamples to a small number (less than a trillion).
A simple computer program that implements Pipletti's classification
theorem for torsion-free Aramaic groups with simplectic socles can
then finish the remaining cases.
\end{abstract}

% TABLE OF CONTENTS, LIST OF FIGURES, LIST OF TABLES
% Please, do not include a table of contents, a list of figures, or a
% list of tables. They will be removed by the editors (and the command
% is actually redefined in the ct.sty file).

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\section{Introduction}

The reconstruction conjecture states that the multiset of unlabeled
vertex-deleted subgraphs of a graph determines the graph, provided it
has at least three vertices. This problem was independently introduced
by Ulam~\cite{Ulam} and Kelly~\cite{Kelly}. The reconstruction
conjecture is widely studied
\cite{Bollobas,FGH,HHRT,KSU,WS} and is very interesting
because it is. See \cite{BH} for more about the
reconstruction conjecture.

\begin{definition}
A graph is \emph{fabulous} if \emph{rest of definition here}.
\end{definition}

\begin{theorem}\label{Thm:FabGraphs}
All planar graphs are fabulous.
\end{theorem}

\begin{proof}
Suppose on the contrary that some planar graph is not fabulous.
Then we have a contradiction.
\end{proof}

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\section{Broglington Manifolds}

This section describes background information about Broglington
Manifolds.

\begin{lemma}\label{lem:Technical}
Broglington manifolds are abundant.
\end{lemma}

\begin{proof}
A proof is given here.
\end{proof}

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\section{Proof of Theorem~\ref{Thm:FabGraphs}}

In this section we complete the proof of Theorem~\ref{Thm:FabGraphs}.

\begin{proof}[Proof of Theorem~\ref{Thm:FabGraphs}]
Let $G$ be a graph. We have
% The align environment for multi-line equations is defined in the amsmath package.
\begin{align}
|X| &= a+b+c \nonumber\\
&= \alpha\beta\gamma.
\end{align}
This completes the proof of Theorem~\ref{Thm:FabGraphs}.
\end{proof}

\begin{figure}[ht]
\centering
% Use \includegraphics to import figures; for example
% \includegraphics[scale=0.6]{filename}
\caption{Here is an informative figure.\label{fig:InformativeFigure}}
\end{figure}

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% ACKNOWLEDGEMENTS
% Include acknowledgements to colleagues and referee here.
% Funding and grant support should appear in footnotes on the front page, using the
% thanks command in the authors command (see above).

\section*{Acknowledgements}

Thanks to Professor Qwerty for suggesting the proof of
Lemma~\ref{lem:Technical} and introducing us to the work of~\cite{Bj95}
as well as~\cite{winter}.

Some of the computation of the present paper have been done using the
SageMath software~\cite{sage}. You can find our code over here~\cite{code}.

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