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Extended MSO Model Checking via Small Vertex Integrity

Authors Tatsuya Gima , Yota Otachi

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • vertex integrity
  • monadic second-order logic
  • cardinality constraint
  • fixed-parameter tractability

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Abstract

We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSO^GL_Lin, introduced recently by Knop, Koutecký, Masařík, and Toufar [Log. Methods Comput. Sci., 15(4), 2019]. We show that the problem is fixed-parameter tractable parameterized by vertex integrity, where vertex integrity is a graph parameter standing between vertex cover number and treedepth. Our result thus narrows the gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.

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Tatsuya Gima and Yota Otachi. Extended MSO Model Checking via Small Vertex Integrity. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ISAAC.2022.20

Author Details

Tatsuya Gima
  • Nagoya University, Japan
Yota Otachi
  • Nagoya University, Japan

Funding

  • Otachi, Yota: JSPS KAKENHI Grant Numbers JP18H04091, JP18K11168, JP18K11169, JP20H05793, JP21K11752, JP22H00513.

Acknowledgements

The authors thank Michael Lampis and Valia Mitsou for fruitful discussions and sharing a preliminary version of [Michael Lampis and Valia Mitsou, 2021].

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