Résumé
A 2-distance-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2- distance (A1)-coloring for graphs with maximum average degree less than and maximum degree A 7. As a corollary, every planar graph with girth at least 9 and A7 admits a 2-distance (A+1)-coloring. The proof uses the potential method to reduce new configurations compared to classic approaches on 2-distance coloring. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, Al training, and similar technologies.