Revisiting Linear Width: Rethinking the Relationship between Single Ideal and Linear Obstacle
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
The study of graph width parameters holds significant importance in the fields of graph theory and combinatorics. Among these parameters, linear-width stands out as a well-established and esteemed measure. The notions of single Ideal and Linear obstacle act as obstacles to achieving optimal linear-width in a connectivity system. In this succinct paper, we offer an alternative proof establishing the equivalence between single ideal and linear obstacle.
Keywords: Linear width, single ideal, linear obstacle, connectivity system