  In the context of branch-and-bound (B&B) for integer programming (IP)
problems, a direction along which the polyhedron of the IP has minimum width is
termed a thin direction. We demonstrate that a thin direction need not always
be a good direction to branch on for solving the problem efficiently. Further,
the integer width, which is the number of B&B nodes created when branching on
the direction, may also not be an accurate indicator of good branching
directions.
