The DP-coloring of the square of subcubic graphs

The 2-distance coloring of a graph G is equivalent to the proper coloring of its square graph G², it is a special distance labeling problem. DP-coloring (or "Correspondence coloring") was introduced by Dvo{r}\'ak and Postle in 2018, to answer a conjecture of list coloring proposed by Borodin. In recent years, many researches pay attention to the DP-coloring of planar graphs with some restriction in cycles. We study the DP-coloring of the square of subcubic graphs in terms of maximum average degree mad(G), and by the discharging method, we showed that: for a subcubic graph G, if mad(G)<9/4, then G² is DP-5-colorable; if mad(G)<12/5, then G² is DP-6-colorable. And the bound in the first result is sharp.