  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 Bacs\'{o}~et~al. ({\em The robust
chromatic number of graphs}, arXiv preprint no. 2305.01923).
