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.
arXiv:2302.01808v1
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The work develops properties of ultrafilters, prefilters, and related notions on connectivity systems while surveying a range of graph width, length, and depth parameters.
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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.
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Various Properties of Various Ultrafilters, Various Graph Width Parameters, and Various Connectivity Systems (with Survey)
The work develops properties of ultrafilters, prefilters, and related notions on connectivity systems while surveying a range of graph width, length, and depth parameters.