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 [WG 2014, JGT 2016].
Cite
@article{arxiv.1905.00340,
title = {Independent Set Reconfiguration Parameterized by Modular-Width},
author = {Rémy Belmonte and Tesshu Hanaka and Michael Lampis and Hirotaka Ono and Yota Otachi},
journal= {arXiv preprint arXiv:1905.00340},
year = {2019}
}