Constant-factor approximation of maximum distance-2 independent set in graphs of bounded merge-width

We give a constant-factor approximation algorithm for Max Dist-2 Independent Set in graphs of bounded radius-2 merge-width. The same result holds for Min Dominating Set from [Bonamy and Geniet, 2025], [Chan et al., SODA '12]. Both approximation algorithms are LP-based, showing that the domination-to-2-independence ratio is bounded in graphs of bounded radius-2 merge-width. Moreover, this result is tight in the sense that the ratio can be unbounded in graphs of bounded radius-1 merge-width.