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- W3136458002 abstract "We study the problem of finding a maximum cardinality minimal separator of a graph. This problem is known to be NP-hard even for bipartite graphs. In this paper, we strengthen this hardness by showing that for planar bipartite graphs, the problem remains NP-hard. Moreover, for co-bipartite graphs and for line graphs, the problem also remains NP-hard. On the positive side, we give an algorithm deciding whether an input graph has a minimal separator of size at least k that runs in time 2 O ( k ) n O ( 1 ) . We further show that there is no 2 o ( n ) n O ( 1 ) -time algorithm unless the Exponential Time Hypothesis (ETH) fails. Finally, we discuss a lower bound for polynomial kernelizations of this problem." @default.
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- W3136458002 date "2021-04-01" @default.
- W3136458002 modified "2023-09-28" @default.
- W3136458002 title "Finding a maximum minimal separator: Graph classes and fixed-parameter tractability" @default.
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- W3136458002 doi "https://doi.org/10.1016/j.tcs.2021.03.006" @default.
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