Improve the lower bound for temporal graphs whose snapshots are paths

Establish whether temporal graphs whose every snapshot is a path admit an exploration-time lower bound asymptotically exceeding Ω(n log n).

Background

The paper describes a construction with path snapshots that yields an Ω(n log n) lower bound. It notes that when the paths are fixed during each phase, an agent can visit all vertices within O(n) steps, limiting the number and duration of useful phases in that scheme.

The cited Ω(n log n) bound is the best known for snapshots that are paths. The authors explicitly leave open whether a stronger lower bound is possible.