Identify graph classes with coinciding submodular and simpler widths

Identify natural classes of graphs for which submodular width coincides with one or more simpler notions of width.

Background

The constructed graph demonstrates strict separation among adaptive, normal, linear, entropic, and submodular widths. The paper therefore asks when such separations disappear for restricted graph families.

The authors suggest that graph classes with coinciding width notions, combined with suitable fine-grained reductions, could be candidates for patterns whose exact computational complexity can be characterized by matching upper and lower bounds.