@article{0d0f7d9355634b91a21762e3e90d0708,
title = "Independent Set Reconfiguration Parameterized by Modular-Width",
abstract = "Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma (J Graph Theory 83(2):164–195, 2016).",
author = "R{\'e}my Belmonte and Tesshu Hanaka and Michael Lampis and Hirotaka Ono and Yota Otachi",
note = "Funding Information: Partially supported by JSPS and MAEDI under the Japan-France Integrated Action Program (SAKURA) Project GRAPA 38593YJ, and by JSPS/MEXT KAKENHI Grant Numbers JP24106004, JP17H01698, JP18K11157, JP18K11168, JP18K11169, JP18H04091, JP18H06469. A preliminary version appeared in the proceedings of the 45th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2019), Lecture Notes in Computer Science 11789 (2019) 285?297. Funding Information: Partially supported by JSPS and MAEDI under the Japan-France Integrated Action Program (SAKURA) Project GRAPA 38593YJ, and by JSPS/MEXT KAKENHI Grant Numbers JP24106004, JP17H01698, JP18K11157, JP18K11168, JP18K11169, JP18H04091, JP18H06469. A preliminary version appeared in the proceedings of the 45th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2019), Lecture Notes in Computer Science 11789 (2019) 285–297. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2020",
month = sep,
day = "1",
doi = "10.1007/s00453-020-00700-y",
language = "English",
volume = "82",
pages = "2586--2605",
journal = "Algorithmica",
issn = "0178-4617",
publisher = "Springer New York",
number = "9",
}