Reconsideration of Tangle and Ultrafilter using Separation and Partition

05/07/2023

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by   Takaaki Fujita, et al.

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