List 2-distance \((\varDelta +2)\)-coloring of planar graphs with girth six (Q1024323)

Suppose each vertex of a graph \(G\) is assigned a list of at least \(k\) admissible colors; then \(G\) is said to be list 2-distance \(k\)-colorable if, for any such collection of lists, it is possible to give each vertex one of its admissible colors in such a way that any two vertices at distance at most two apart receive different colors. The authors show that any planar graph with girth at least 6 and maximum degree \(D\) at least 36 is list 2-distance \((D+2)\)-colorable.