Identify additional parameters coarsely equivalent to path-length

Identify other interesting graph parameters that are coarsely equivalent to the path-length of a graph.

Background

The paper introduces and relates several parameters that characterize bounded path-length, including domination parameters, power indices, caterpillar distortion, McCarty index, minor fatness, and BFS-layering quantities. It remains unresolved whether further natural graph parameters admit universal constant-factor equivalence with path-length.

References

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

— Graph parameters that are coarsely equivalent to path-length  (2503.05661 - Dragan et al., 7 Mar 2025) in Section 5, “Concluding remarks and open questions”