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\title{Graph Theory}
\author{By Lars Noschinski}
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\begin{abstract}
This development provides a formalization of planarity based on combinatorial maps and proves that Kuratowski's theorem implies combinatorial planarity.
Moreover, it contains verified implementations of programs checking certificates for planarity (i.e., a combinatorial map) or non-planarity (i.e., a Kuratowski subgraph).

The development is described in \cite{noschinski_formalizing_2015}.
\end{abstract}


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