Finding a maximum minimal separator: Graph classes and fixed-parameter tractability

Tesshu Hanaka, Yasuaki Kobayashi, Yusuke Kobayashi, Tsuyoshi Yagita

Research output: Contribution to journalArticlepeer-review


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 2O(k)nO(1). We further show that there is no 2o(n)nO(1)-time algorithm unless the Exponential Time Hypothesis (ETH) fails. Finally, we discuss a lower bound for polynomial kernelizations of this problem.

Original languageEnglish
Pages (from-to)131-140
Number of pages10
JournalTheoretical Computer Science
Publication statusPublished - Apr 14 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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