Extended MSO Model Checking via Small Vertex Integrity

02/17/2022

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by   Tatsuya Gima, et al.

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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 fill a gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.