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.
Abstract Separation Systems
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abstract
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree structure theorems in graphs, matroids or CW-complexes to, potentially, image segmentation and cluster analysis. This paper is intended as a concise common reference for the basic definitions and facts about abstract separation systems in these and any future papers using this framework.
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math.CO 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
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Optimal trees of tangles: refining the essential parts
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.