Note on robust coloring of planar graphs

We consider the robust chromatic number $χ_1(G)$ of planar graphs $G$ and show that there exists an infinite family of planar graphs $G$ with $χ_1(G) = 3$, thus solving a recent problem of Bacsó~et~al. (The robust chromatic number of graphs, Graphs Combin. 40 (2024), #89).