### Abstract

We present a formalization of flow networks and the Min-Cut-Max-Flow theorem. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL, the interactive theorem prover used for the formalization.

### License

BSD License

### Topics

- Mathematics/Graph theory

### Session Flow_Networks

- Fofu_Abs_Base
- Fofu_Impl_Base
- Refine_Add_Fofu
- Graph
- Network
- Residual_Graph
- Augmenting_Flow
- Augmenting_Path
- Ford_Fulkerson
- Graph_Impl
- Network_Impl
- NetCheck

### Depends on

- The CAVA Automata Library
- A Framework for Verifying Depth-First Search Algorithms
- Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors
- The Imperative Refinement Framework

### Used by

- Formalizing Push-Relabel Algorithms
- Formalizing the Edmonds-Karp Algorithm

### Auto-related entries

- Formalizing the Edmonds-Karp Algorithm
- Formalizing Push-Relabel Algorithms
- Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL
- A Verified Imperative Implementation of B-Trees
- Pop-Refinement

## Cite

×

Flow_Networks-AFP

    @article{Flow_Networks-AFP,
      author  = {Peter Lammich and S. Reza Sefidgar},
      title   = {Flow Networks and the Min-Cut-Max-Flow Theorem},
      journal = {Archive of Formal Proofs},
      month   = {June},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Flow_Networks.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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