We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSOLinGL, introduced recently by Knop, Kouteck\'{y}, Masa\v{r}\'{i}k, 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.
@article{arxiv.2202.08445,
title = {Extended MSO Model Checking via Small Vertex Integrity},
author = {Tatsuya Gima and Yota Otachi},
journal= {arXiv preprint arXiv:2202.08445},
year = {2023}
}