Determine the exact entropic width of the 32-vertex separating graph

Determine the exact entropic width of the 32-vertex graph G, whose entropic width is currently bounded by 635/101 and 183/29.

Background

The paper constructs a 32-vertex graph whose adaptive, normal, linear, entropic, and submodular widths are separated. The adaptive, normal, linear, and submodular widths are determined exactly, but the entropic width is only bounded between 635/101 and 183/29.

The lower bound is obtained from an explicit almost entropic polymatroid, while the upper bound follows from the Zhang–Yeung inequality. The authors explain that the corresponding optimization over almost entropic polymatroids cannot be settled by linear programming because the almost-entropic cone is not a polyhedron.