Profiles. An algebraic approach to combinatorial connectivity

Details Profiles. An algebraic approach to combinatorial connectivity Profiles. An algebraic approach to combinatorial connectivity

2011-10-27

arxiv.org/abs/1110.6207v1

Mathematics

Combinatorics

Scientific paper

We describe an algebraic approach to combinatorial connectivity. As an application, we obtain canonical tree-decompositions distinguishing all the maximal tangles of a finite graph or matroid. For graphs we also find such decompositions which, for any given k, distinguish all their distinguishable k-blocks and tangles of order k+1. If we only consider robust blocks and tangles, we obtain one overall tree-decomposition which refines all these tree-decompositions, for all k simultaneously.

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