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Extended MSO Model Checking via Small Vertex Integrity

Algorithmica, ISSN: 1432-0541, Vol: 86, Issue: 1, Page: 147-170
2024
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Article Description

We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSOLinGL , introduced recently by Knop et al. (Log Methods Comput Sci, 15(4), 2019. https://doi.org/10.23638/LMCS-15(4:12)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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