Polynomial-time algorithms for induced covering numbers

Determine whether algorithms for computing non-induced covering numbers, especially local covering numbers, can be adapted to compute the corresponding induced covering numbers.

Background

Some non-induced covering numbers, including local star arboricity, can be computed in polynomial time. The paper explains that boundedness can then yield approximation algorithms for induced covering numbers, but exact computation remains unresolved. It explicitly asks whether the existing algorithms can be adapted to the induced setting.

References

Can the algorithms for covering numbers be adapted to determine induced covering numbers?

— Boundedness and Separation Between Induced and Non-Induced Covering Numbers  (2609.09873 - Goetze et al., 9 Sep 2026) in Section 5, subsection “Algorithms and Complexity”