Canonical tree-decompositions of finite graphs II. Essential parts

Johannes Carmesin, Reinhard Diestel, Matthias Hamann, Fabian Hundertmark

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
139 Downloads (Pure)


In Part I of this series we described three algorithms that construct canonical tree-decompositions of graphs which distinguish all their k-blocks and tangles of order k. We now establish bounds on the number of parts in these decompositions that contain no such block or tangle, and determine conditions under which such parts contain nothing but a k-block.
Original languageEnglish
Pages (from-to)268-283
JournalJournal of Combinatorial Theory. Series B
Early online date28 Aug 2015
Publication statusPublished - May 2016

Bibliographical note

15 pages, 3 figures


  • math.CO
  • graph
  • minor
  • tangle k-block
  • tree-decomposition


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