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Temporal graph classes: a view through temporal separators. (English) Zbl 1436.68234
Summary: We investigate for temporal graphs the computational complexity of separating two distinct vertices $$s$$ and $$z$$ by vertex deletion. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding Temporal $$(s, z)$$-Separation problem is NP-complete, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph – there we observe polynomial-time solvability in the case of bounded treewidth – as well as restrictions concerning the “temporal evolution” along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68Q25 Analysis of algorithms and problem complexity 68Q27 Parameterized complexity, tractability and kernelization
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