Other parameters coarsely equivalent to tree-length

Identify additional natural graph parameters that are coarsely equivalent to tree-length.

Background

The paper establishes coarse equivalence between tree-length and numerous parameters, including layering-partition parameters, embedding distortions, separator parameters, bramble interception radii, fat-minor parameters, and cycle parameters. It explicitly leaves open whether further interesting graph parameters belong to this same coarse-equivalence class.

References

Are there any other interesting graph parameters that are coarsely equivalent to tree-length?

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