Algorithms Parameterized by Vertex Cover and Modular Width, Through Potential Maximal Cliques

@article{Fomin2017AlgorithmsPB,
  title={Algorithms Parameterized by Vertex Cover and Modular Width, Through Potential Maximal Cliques},
  author={Fedor V. Fomin and Mathieu Liedloff and Pedro Montealegre-Barba and Ioan Todinca},
  journal={Algorithmica},
  year={2017},
  volume={80},
  pages={1146-1169}
}
  • Fedor V. Fomin, Mathieu Liedloff, +1 author Ioan Todinca
  • Published in Algorithmica 2017
  • Computer Science, Mathematics
  • In this paper we give upper bounds on the number of minimal separators and potential maximal cliques of graphs w.r.t. two graph parameters, namely vertex cover ($${\text {vc}}$$vc) and modular width ($${\text {mw}}$$mw). We prove that for any graph, the number of its minimal separators is $${\mathcal {O}}^*(3^{{\text {vc}}})$$O∗(3vc) and $${\mathcal {O}}^*(1.6181^{{\text {mw}}})$$O∗(1.6181mw), and the number of potential maximal cliques is $${\mathcal {O}}^*(4^{{\text {vc}}})$$O∗(4vc) and… CONTINUE READING

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