Complexity and inapproximability of the remaining parameters

Determine the computational complexity of computing the McCarty index and the $(K_3,K_{1,3})$-minor fatness index, and establish whether nontrivial inapproximability results hold for these parameters.

Background

The paper distinguishes parameters that are NP-hard to compute exactly from parameters admitting polynomial-time algorithms and constant-factor approximation procedures. It introduces the McCarty index and the $(K_3,K_{1,3})$-minor fatness index as additional coarse equivalents of path-length, but does not provide a complete complexity or approximation classification for them. The concluding question asks for both algorithmic complexity results and hardness-of-approximation results.