Minimal token-sliding augmentation for pancyclicity

Determine whether a smaller addition of token-sliding edges to the dominating graph can induce pancyclicity in the associated domination reconfiguration graph.

Background

A TARS-graph is formed by augmenting the dominating graph, which uses token addition/removal edges, with token-sliding edges. The paper observes that only a small number of token-sliding edges are used at a time in the proofs establishing pancyclicity for the studied graph classes. This raises the unresolved question of whether the full set of token-sliding edges is necessary, or whether a smaller augmentation can produce the same pancyclicity property.