Inc-max ordering on k-degenerate graphs

Determine the computational complexity of the inc-max vertex-ordering problem restricted to k-degenerate graphs for integers k≥2.

Background

The paper establishes NP-hardness of both dec-min and inc-max k-bounded ordering for every integer k≥2k\ge 2. It notes that this also establishes NP-hardness of dec-min ordering on k-degenerate graphs with k≥2k\ge2.

The corresponding complexity of inc-max ordering on the broader class of k-degenerate graphs is not settled by the bounded-order results, because an optimal inc-max ordering need not itself satisfy the same k-bound.

References

However, the complexity of the inc-max problem for $k$\nobreakdash-degenerate graphs remains unresolved.

— Separable convex optimization over indegree polytopes  (2509.06182 - Borsik et al., 7 Sep 2025) in Section 6, Open questions; following the results of Section 4 (Section~\ref{sec:decMinIncMax})