Deciding existence of a temporally connected subgraph on at least 3 vertices is NP-hard for directed/undirected and strict/non-strict temporal graphs via simple and proper reductions.
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On the Hardness of Finding Temporally Connected Subgraphs of Any Size
Deciding existence of a temporally connected subgraph on at least 3 vertices is NP-hard for directed/undirected and strict/non-strict temporal graphs via simple and proper reductions.