Coarse equivalence of relaxed cycle-bridging parameters

Determine whether there exists a universal constant c such that the relaxed bridging non-locally geodesic cycles parameter of every graph G is at most c times the bridging non-locally geodesic cycles constant of G.

Background

The paper introduces a bridging non-locally geodesic cycles constant and then considers a further relaxed cycle condition requiring a bridge in general position. The relaxed parameter is immediately shown to be no larger than the original one, but no converse coarse bound is established.