List 2-distance -coloring of planar graphs with girth six

It was proved in [Z.Dvořàk, D.Kràl, P.Nejedlỳ, R.Škrekovski, Coloring squares of planar graphs with girth six, European J. Combin. 29 (4) (2008) 838–849] that every planar graph with girth g ≥ 6 and maximum degree Δ ≥ 8821 is 2-distance ( Δ + 2 ) -colorable. We prove that every planar graph with g ≥ 6 and Δ ≥ 36 is list 2-distance ( Δ + 2 ) -colorable.