interval thickness | node searching number | separation number | vertex searching number | vertex separation number

The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path decomposition G. As summarized in the table below, obstruction sets for pathwidth <=1 (consisting of the triangle graph C_3 and spoke graph S(3, 2), illustrated above) and <=2 (consisting of 110 graphs) were described in Kinnersley and Langston taking advantage of the fact that gate matrix layout with parameter k is identical to the pathwidth problem with parameter k - 1 (Fellows and Langston 1989, Kinnersley and Langston 1992).

graph bandwidth | spoke graph | treewidth