### Abstract

We present a formalization of Menger's Theorem for directed and undirected graphs in Isabelle/HOL. This well-known result shows that if two non-adjacent distinct vertices u, v in a directed graph have no separator smaller than n, then there exist n internally vertex-disjoint paths from u to v. The version for undirected graphs follows immediately because undirected graphs are a special case of directed graphs.

### License

BSD License

### Topics

- Mathematics/Graph theory

### Session Menger

- Helpers
- Graph
- Separations
- DisjointPaths
- MengerInduction
- Y_eq_new_last
- Y_neq_new_last
- Menger

## Cite

×

Menger-AFP

    @article{Menger-AFP,
      author  = {Christoph Dittmann},
      title   = {Menger's Theorem},
      journal = {Archive of Formal Proofs},
      month   = {February},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Menger.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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