Independent Set Reconfiguration Parameterized by Modular-Width

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 $${\mathsf {TAR}}$$, $${\mathsf {TJ}}$$, and $${\mathsf {TS}}$$. The result under $${\mathsf {TAR}}$$ resolves an open problem posed by Bonsma (J Graph Theory 83(2):164–195, 2016).