Extended MSO Model Checking via Small Vertex Integrity

Abstract

We study the model checking problem of an extended $\mathsf{MSO}$ with local and global cardinality constraints, called ${\mathsf{MSO}}_{\mathsf{Lin}}^{\mathsf{GL}}$, 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 narrows the gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.

References in corpus (1)

• Fine-grained Meta-Theorems for Vertex Integrity