Distance-2 Edge Coloring is NP-Complete

Let G be a simple, undirected graph. We say that two edges of G are within distance 2 of each other if either they are adjacent or there is some other edge that is adjacent to both of them. A distance-2-edge-coloring of G is an assignment of colors to edges so that any two edges within distance 2 of each other have distinct colors, or equivalently, a vertex-coloring of the square of the line graph of G. If the coloring uses only k colors, it is called a k-D2-edge-coloring, and the graph G is said to be k-D2-edge-colorable. Any k-D2-edge-colorable graph is also (k + 1)-D2-edge-colorable.