Improvement of coarse-equivalence constants

Determine whether the constants in the established inequalities relating the graph parameters coarsely equivalent to path-length can be further improved.

Background

The paper proves a network of explicit constant-factor inequalities between path-length and parameters including path-breadth, strong path-breadth, caterpillar-tree additive distortion, power indices, domination parameters, the McCarty index, and the fat-minor index. The authors ask whether these numerical constants are optimal or can be reduced, including the examples mentioned in the surrounding discussion.