Coloring squares of planar graphs with small maximum degree

Mateusz Krzyziński, Paweł Rzążewski, Szymon Tur

For a graph $G$, by ${\chi }_2(G)$ we denote the minimum integer $k$, such that there is a $k$-coloring of the vertices of $G$ in which vertices at distance at most 2 receive distinct co…