# Extended MSO Model Checking via Small Vertex Integrity

arXiv: https://arxiv.org/abs/2202.08445 · HTML: https://mlsanity.com/paper/2202.08445/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2022.

## Built on by (most cited first, 1 of 1)

- [The Computational Complexity of Positive Non-Clashing Teaching in Graphs](https://mlsanity.com/paper/2503.07665/) (2025)

## Abstract (arXiv)

We study the model checking problem of an extended mathsfMSO with local and global cardinality constraints, called mathsfMSO^mathsfGL_mathsfLin, introduced recently by Knop, Kouteck'y, Masavr'ik, 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.