Ultrafilter in Digraph: Directed Tangle and Directed Ultrafilter
Takaaki Fujita *
Graduate School of Science and Technology, Gunma University, 1-5-1 Tenjin-Cho, Kiryu, Gunma 376-8515, Japan.
*Author to whom correspondence should be addressed.
Abstract
Tangle is a concept in graph theory that has a dual relationship with tree-width which is well-known graph width parameter. Ultrafilter is a fundamental notion in mathematics. In this concise paper, we will reconsider the relationship between Tangle and Ultrafilter in digraph.
Keywords: Tangle, directed tangle, ultrafilter, directed ultrafilter, directed tree-decomposition, directed linear-branch-decomposition