Deciding TC spanning tree existence in temporal graphs is NP-complete; bidirectional spanners are testable in P but their minimization is NP-hard, with FPT algorithms via feedback edge set parameterization.
Sparse tempo- ral spanners with low stretch
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In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs
Deciding TC spanning tree existence in temporal graphs is NP-complete; bidirectional spanners are testable in P but their minimization is NP-hard, with FPT algorithms via feedback edge set parameterization.