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 ๐–ฌ๐–ฒ๐–ฎ with local and global cardinality constraints, called ๐–ฌ๐–ฒ๐–ฎ^๐–ฆ๐–ซ_๐–ซ๐—‚๐—‡, introduced recently by Knop, Kouteckรฝ, Masaล™รญk, 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.

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