On algorithmic applications of sim-width and mim-width of (H1,H2)-free graphs

Mim-width and sim-width are among the most powerful graph width parameters, with more than mim-width, which is in turn clique-width. While several NP-hard problems become tractable for classes whose mim-width bounded quickly computable, no algorithmic applications of boundedness known. In Kang et al. (2017) [32], it asked whether Independent Set 3-Colouring NP-complete on graphs at 1. We observe that, each k∈N, List k-Colouring polynomial-time solvable computable. Moreover, we show that if same holds Set, then H-Packing This problem a common generalisation Induced Matching, Dissociation k-Separator. also make progress toward classifying (H1,H2)-free case H1 complete or edgeless. Our results solve some open Brettell (2022) [6].