We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. 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-hard, 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.
@article{arxiv.1803.00882,
title = {Temporal Graph Classes: A View Through Temporal Separators},
author = {Till Fluschnik and Hendrik Molter and Rolf Niedermeier and Malte Renken and Philipp Zschoche},
journal= {arXiv preprint arXiv:1803.00882},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1711.00963