Hardness radius of Max Clique under both graph distances

Determine the hardness radius of Max Clique under both the maximum-degree distance and the edge-edit distance used to define the Sidestep meta-problem.

Background

The paper establishes hardness-radius results for the decision versions of Independent Set, Clique, Vertex Cover, Coloring, and Clique Cover, but explicitly distinguishes these from the optimization versions. For Max Clique, the optimization problem requires the exact clique number of the selected nearby graph, making it substantially different from the threshold decision problem. Its hardness radius under either considered graph distance is left unresolved.

References

What is the hardness radius of Max Clique under $dist$ and under~$dist$?

— Answering Related Questions  (2501.10633 - Bonnet, 18 Jan 2025) in Question 4, Section 1, subsection “Open questions and potential future work”