Canonical tree-decompositions of finite graphs I. Existence and algorithms

Johannes Carmesin, Reinhard Diestel, Matthias Hamann, Fabian Hundertmark

Published 2013-05-20, updated 2014-04-24Version 3

We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject to the requirement that they commute with graph isomorphisms. In particular, all the decompositions constructed are invariant under the automorphisms of the graph.