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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Expository overview of tangle theory from graph connectivity and its potential use for identifying types via co-occurring qualities in quantitative social science data.
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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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Tangles in the social sciences
Expository overview of tangle theory from graph connectivity and its potential use for identifying types via co-occurring qualities in quantitative social science data.