Computer Science:

Graphs with pathwidth k turn out to be the same as those with gate matrix layout cost k + 1. What are the minor-minimal obstructions to pathwidth 1? How many obstructions are there to pathwidth 2? Is it feasible to isolate the obstruction set for pathwidth 3? Explain. Testing for an immersed K_2 is easy. Just check whether a graph has an edge. How would you test for an immersed K_3? How would you test for an immersed K_4? Graphs with pathwidth k turn out to be the same as those with gate matrix layout cost k + 1. What are the minor-minimal obstructions to pathwidth 1? How many obstructions are there to pathwidth 2? Is it feasible to isolate the obstruction set for pathwidth 3? Explain. Testing for an immersed K_2 is easy. Just check whether a graph has an edge. How would you test for an immersed K_3? How would you test for an immersed K_4