Realizability of trees under standard zero forcing

Determine which trees arise as token exchange reconfiguration graphs of minimum standard zero forcing sets.

Background

The paper contrasts the realizability of trees under several zero forcing rules. It proves that, except in trivial cases, no tree can be realized as a PSD token exchange reconfiguration graph, while prior work established realizability results for certain paths under standard zero forcing. The authors explicitly leave the general standard-zero-forcing tree-realizability question unresolved.

References

The realizability of other trees under the standard color change rule is unresolved.

— Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets  (2501.03642 - Bong et al., 7 Jan 2025) in Section 4, subsection “Reconfiguration of Trees”