Hardness of undirected majority-illusion elimination on grid graphs

Determine whether the undirected majority-illusion elimination by recoloring vertices remains NP-hard on grid graphs. Specifically, given an undirected grid graph G, a coloring f: V(G) -> {B, R}, and an integer k, ascertain whether deciding the existence of a recoloring f′ that changes at most k vertices so that no vertex has strictly more red neighbors than blue neighbors is NP-hard on grid graphs.

Background

The paper proves that eliminating majority illusion by recoloring (Difr) is NP-complete on directed grids. It also observes that the same construction implies NP-hardness for the undirected problem on subgraphs of grids.

However, the authors do not establish the complexity for the undirected problem on full grid graphs. They note that edge orientations are crucial in their directed construction for keeping certain vertices under illusion, leaving open whether hardness persists when edges are undirected on grid graphs.

References

However, it is not clear if the undirected version of the problem remains hard on grid graphs.

— Eliminating Illusion in Directed Networks  (2604.02395 - Jana et al., 2 Apr 2026) in Subsection “NP-completeness of Difr on Grid Graphs,” paragraph following Theorem \ref{thm:gridreduction}