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.

我们研究时间图通过顶点删除来分离两个不同的顶点s和z的计算复杂性。在时间图中，顶点集是固定的，但边具有（离散的）时间标签。自从对应时空 $（s，ž）$-分离问题是NP-完全的，很自然地要研究是否存在可计算处理的相关特殊情况。为此，我们研究了基础（静态）图的限制-在树宽有界的情况下，我们观察到多项式时间可解性-以及沿着时间步长的“时间演化”的限制。系统地研究这个方向上的部分新颖概念，我们确定了难处理和难处理的病例之间的明显界限。