Abstract
A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance atmost 2 cannot share the same color. We prove the existence of a 2-distance (∆ + 1)-coloring for graphs withmaximum average degree less than 18 and maximum degree ∆ ≥ 7. As a corollary, every planar graph with 7girth at least 9 and ∆ ≥ 7 admits a 2-distance (∆ + 1)-coloring. The proof uses the potential method to reduce new configurations compared to classic approaches on 2-distance coloring.