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Canonical tree-decompositions of finite graphs. I: Existence and algorithms. (English) Zbl 1327.05269
Summary: 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.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C05 Trees 05C40 Connectivity
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##### References:
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