Tree Decomposition

Christoph Dittmann

31 May 2016

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.
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Theories

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