3 papers
math.CO2023
Exploring two concepts: branch decomposition and weak ultrafilter on connectivity system
Takaaki Fujita
This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch width is a significant graph width parameter that measures the degree of connectivity in a g…
cs.DM2023
Revisiting Linear Width: Rethinking the Relationship between Single Ideal and Linear Obstacle
Takaaki Fujita
Linear-width is a well-known and highly regarded graph parameter. The concept of Single Ideal and Linear obstacle serves as an obstruction to linear-width on a connectivity sysem.…
math.CO2023
Reconsideration of Tangle and Ultrafilter using Separation and Partition
Takaaki Fujita
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 s…