A Graph Library for Isabelle

In contrast to other areas of mathematics such as calculus, number theory or probability theory, there is currently no standard library for graph theory for the Isabelle/HOL proof assistant. We present a formalization of directed graphs and essential related concepts. The library supports general infinite directed graphs (digraphs) with labeled and parallel arcs, but care has been taken not to complicate reasoning on more restricted classes of digraphs. We use this library to formalize a characterization of Euler Digraphs and a to verify a method of checking Kuratowski subgraphs used in the LEDA library. Mathematics Subject Classification (2010). Primary: 05C20, Secondary: 05C45.