For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. This is the problem of coloring the vertices while ensuring that two vertices that are adjacent or have a common neighbor receive different colors. It is already known that planar graphs of girth at least 6 and of maximum degree @D are list 2-distance (@D+2)-colorable when @D>=24 (Borodin and Ivanova (2009)) and 2-distance (@D+2)-colorable when @D>=18 (Borodin and Ivanova (2009)). We prove here that @D>=17 suffices in both cases. More generally, we show that graphs with maximum average degree less than 3 and @D>=17 are list 2-distance (@D+2)-colorable. The proof can be transposed to list injective (@D+1)-coloring.
['Marthe Bonamy', 'Benjamin Lévêque', 'Alexandre Pinlou']
Graphs with maximum degree Δ≥17 and maximum average degree less than 3 are list 2-distance (Δ+2)-colorable