2026-07-25T14:19:31Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17305 2024-03-06T10:59:24Z ddc:004 open_access

Extended MSO Model Checking via Small Vertex Integrity Gima, Tatsuya Otachi, Yota vertex integrity monadic second-order logic cardinality constraint fixed-parameter tractability We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSO^GL_Lin, 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tatsuya Gima and Yota Otachi 2022 Is Part Of LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2022.20 urn:nbn:de:0030-drops-173056 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.20 eng https://creativecommons.org/licenses/by/4.0/legalcode