2-Distance List (Δ+3)-Coloring of Sparse Graphs

A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex has a list of at least k available colors and vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance list (Delta + 3)-coloring for graphs with maximum average degree less than 8/3 and maximum degree Delta >= 4 as well as graphs with maximum average degree less than 14/5 and maximum degree Delta >= 6.