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Tangle is a concept in graph theory that has a dual relationship withbranch-width which is well-known graph width parameter. Ultrafilter, afundamental notion in mathematics, is similarly known to have a dualrelationship with branch-width when extended to a connectivity system (X, f).We will reconsider these concepts using separation and partition.

Reconsideration of Tangle and Ultrafilter using Separation and Partition