Revisiting Linear Width: Rethinking the Relationship between Single Ideal and Linear Obstacle

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.