Coarse equivalence of strong tree-breadth and tree-breadth

Determine whether there exists a universal constant c such that the strong tree-breadth of every graph G is at most c times its tree-breadth.

Background

Strong tree-breadth requires every bag in a tree-decomposition to equal a graph disk centered at a vertex of that bag, while ordinary tree-breadth only requires each bag to be contained in such a disk. The paper notes the immediate inequality from strong tree-breadth to tree-breadth and explicitly asks whether the two parameters are coarsely equivalent.

References

Does there exist a constant c such that (G)\le c\cdot(G) for every graph G?

— Graph parameters that are coarsely equivalent to tree-length  (2502.00951 - Dragan, 2 Feb 2025) in Section 4, “Concluding remarks and open questions,” Question 4