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\title{Graph Theory}
\author{By Lars Noschinski}
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\begin{abstract}
This development provides a formalization of directed graphs, supporting
(labelled) multi-edges and infinite graphs. A polymorphic edge type allows
edges to be treated as pairs of vertices, if multi-edges are not required.
Formalized properties are i.a. walks (and related concepts), connectedness and
subgraphs and basic properties of isomorphisms.

This formalization is used to prove characterizations of Euler Trails, Shortest
Paths and Kuratowski subgraphs.

Definitions and nomenclature are based on \cite{bangjensen2009digraphs}.
\end{abstract}


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