pith. sign in

arxiv: 1110.6207 · v5 · pith:3K7DS6JGnew · submitted 2011-10-27 · 🧮 math.CO

Profiles of separations: in graphs, matroids and beyond

classification 🧮 math.CO
keywords theoremgraphmatroidabstractanalysisanotherapplicationsapplying
0
0 comments X
read the original abstract

We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem for more general combinatorial structures, which has further applications. These include a new approach to cluster analysis and image segmentation. As another illustration for the abstract theorem, we show that applying it to edge-tangles yields the Gomory-Hu theorem.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Optimal trees of tangles: refining the essential parts

    math.CO 2023-04 unverdicted novelty 7.0

    A single theorem showing that any efficient k-tangle-distinguishing tree-decomposition of a graph can be refined so each part is either too small for a k-tangle or minimal while containing one.