### Abstract

We formalize tree decompositions and tree width in Isabelle/HOL, proving that trees have treewidth 1. We also show that every edge of a tree decomposition is a separation of the underlying graph. As an application of this theorem we prove that complete graphs of size n have treewidth n-1.

### License

BSD License

### Topics

- Mathematics/Graph theory

### Session Tree_Decomposition

- Graph
- Tree
- TreeDecomposition
- TreewidthTree
- TreewidthCompleteGraph
- ExampleInstantiations

## Cite

×

Tree_Decomposition-AFP

    @article{Tree_Decomposition-AFP,
      author  = {Christoph Dittmann},
      title   = {Tree Decomposition},
      journal = {Archive of Formal Proofs},
      month   = {May},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/Tree_Decomposition.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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