Note on robust coloring of planar graphs

We consider the robust chromatic number ${\chi }_1(G)$ of planar graphs $G$ and show that there exists an infinite family of planar graphs $G$ with ${\chi }_1(G)=3$, thus solving a recent problem of Bacsó~et~al. (The robust chromatic number of graphs, Graphs Combin. 40 (2024), #89).