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\title{\bf An elementary proof\\ of the reconstruction conjecture}
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\author{Dagwood Remifa\thanks{Supported by NASA grant ABC123.}\\
\small Department of Inconsequential Studies\\[-0.8ex]
\small Solatido College\\[-0.8ex]
\small North Kentucky, U.S.A.\\
\small\tt remifa@dis.solatido.edu\\
\and
Forgotten Second Author \qquad Forgotten Third Author\\
\small School of Hard Knocks\\[-0.8ex]
\small University of Western Nowhere\\[-0.8ex]
\small Nowhere, Australasiaopia\\
\small\tt \{fsa,fta\}@uwn.edu.ao
}
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\date{\dateline{Jan 1, 2012}{Jan 2, 2012}\\
\small Mathematics Subject Classifications: 05C88, 05C89}
\begin{document}
\maketitle
% E-JC papers must include an abstract. The abstract should consist of a
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\begin{abstract}
The reconstruction conjecture states that the multiset of unlabeled
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.
% keywords are optional
\bigskip\noindent \textbf{Keywords:} graph reconstruction
conjecture; Broglington manifold; Pipletti's classification
\end{abstract}
\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 independtly introduced
by Ulam~\cite{Ulam} and Kelly~\cite{Kelly}. The reconstruction
conjecture is widely studied
\cite{Bollobas,FGH,HHRT,KSU,RM,RR,Stockmeyer} and is very interesting
because...... See \cite{WikipediaReconstruction} for more about the
reconstruction conjecture.
\begin{definition}
A graph is \emph{fabulous} if....
\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....
\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}
\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... Hence
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|X| &= abcdefghijklmnopqrstuvwxyz \nonumber\\
&= \alpha\beta\gamma
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This completes the proof of Theorem~\ref{Thm:FabGraphs}.
\end{proof}
\begin{figure}[!h]
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\caption{\label{fig:InformativeFigure} Here is an informative
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\subsection*{Acknowledgements}
Thanks to Professor Querty for suggesting the proof of
Lemma~\ref{lem:Technical}.
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\begin{thebibliography}{10}
\bibitem{Bollobas} B{\'e}la Bollob{\'a}s. \newblock Almost every
graph has reconstruction number three. \newblock {\em J. Graph
Theory}, 14(1):1--4, 1990.
\bibitem{WikipediaReconstruction} Wikipedia contributors. \newblock
Reconstruction conjecture. \newblock {\em Wikipedia, the free
encyclopedia}, 2011.
\bibitem{FGH} J.~Fisher, R.~L. Graham, and F.~Harary. \newblock A
simpler counterexample to the reconstruction conjecture for
denumerable graphs. \newblock {\em J. Combinatorial Theory Ser. B},
12:203--204, 1972.
\bibitem{HHRT} Edith Hemaspaandra, Lane~A. Hemaspaandra,
Stanis{\l}aw~P. Radziszowski, and Rahul Tripathi. \newblock
Complexity results in graph reconstruction. \newblock {\em Discrete
Appl. Math.}, 155(2):103--118, 2007.
\bibitem{Kelly} Paul~J. Kelly. \newblock A congruence theorem for
trees. \newblock {\em Pacific J. Math.}, 7:961--968, 1957.
\bibitem{KSU} Masashi Kiyomi, Toshiki Saitoh, and Ryuhei Uehara.
\newblock Reconstruction of interval graphs. \newblock In {\em
Computing and combinatorics}, volume 5609 of {\em Lecture Notes in
Comput. Sci.}, pages 106--115. Springer, 2009.
\bibitem{RM} S.~Ramachandran and S.~Monikandan. \newblock Graph
reconstruction conjecture: reductions using complement, connectivity
and distance. \newblock {\em Bull. Inst. Combin. Appl.},
56:103--108, 2009.
\bibitem{RR} David Rivshin and Stanis{\l}aw~P. Radziszowski.
\newblock The vertex and edge graph reconstruction numbers of small
graphs. \newblock {\em Australas. J. Combin.}, 45:175--188, 2009.
\bibitem{Stockmeyer} Paul~K. Stockmeyer. \newblock The falsity of the
reconstruction conjecture for tournaments. \newblock {\em J. Graph
Theory}, 1(1):19--25, 1977.
\bibitem{Ulam} S.~M. Ulam. \newblock {\em A collection of
mathematical problems}. \newblock Interscience Tracts in Pure and
Applied Mathematics, no. 8. Interscience Publishers, New
York-London, 1960.
\end{thebibliography}
\end{document}