2-distance 4-coloring of planar subcubic graphs with girth at least 21

A 2-distance k-coloring of a graph is a proper vertex k-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance 4-coloring for planar subcubic graphs with girth at least 21. We also show a construction of a planar subcubic graph of girth 11 that is not 2-distance 4-colorable. Comment: 21 pages, 14 figures