List 2-distance $(\Delta+1)$-coloring of planar graphs with girth at least 7

A trivial lower bound for the 2-distance chromatic number $\chi_2(G)$ of every graph $G$ with maximum degree $\Delta$ is $\Delta+1$. There are graphs with arbitrarily large $\Delta$ and girth $g\le6$ having $\chi_2(G)\ge\Delta+2$. In the paper are improved previously known restrictions on $\Delta$ and $g$ under which every planar graph $G$ has $\chi_2(G)=\Delta+1$. Ill. 2, bibliogr. 24.