Maximum token-sliding augmentation without pancyclicity

Determine how many token-sliding edges can be added to a dominating graph while avoiding pancyclicity in the resulting reconfiguration graph.

Background

Adding token-sliding edges can induce pancyclicity in dominating graphs that otherwise never have Hamilton cycles. The paper asks not only how many such edges are sufficient, but also how many can be present before pancyclicity becomes unavoidable.

A general upper bound or characterization of token-sliding edge sets that do not induce pancyclicity remains unresolved.