List 2-distance (Δ + 1)-coloring of planar graphs with girth at least 7
Anna O. Ivanova · Journal of Applied and Industrial Mathematics · 2011
The trivial lower bound for the 2-distance chromatic number χ 2(G) of a graph G with maximum degree Δ is Δ + 1. There are available some examples of the graphs with girth g ≤ 6 that have arbitrarily large Δ and χ 2(G) ≥ Δ + 2. In the paper we improve the known restrictions on Δ and g under which a planar graph G has χ 2(G) = Δ + 1.