Maximum token-sliding augmentation preserving non-pancyclicity

Determine how many token-sliding edges can be added to a dominating graph without inducing pancyclicity in the resulting reconfiguration graph.

Background

The paper asks not only how many token-sliding edges are sufficient to produce pancyclicity, but also how much token-sliding augmentation can be tolerated while the resulting reconfiguration graph remains non-pancyclic. This seeks quantitative limits on the effect of adding token-sliding adjacencies to the dominating graph.

References

Or, on the other hand, how many could be included without inducing pancyclicity?

— On Pancyclicity in a Mixed Model for Domination Reconfiguration  (2502.17227 - Messinger et al., 24 Feb 2025) in Section 4, Open Questions