On the Anderson-Lipman conjecture and some related problems

Anderson and Lipman defined the wreath product and conjectured that the edge-chromatic number of GρH is of class 1 if G is of class 1. In the same paper, they asked about the edge-chromatic number of GρP2 and they hinted that this is probably difficult where P2 is a path of order 2. In this paper we prove that GρP2 is of class 1 for any graph G and prove that GρH is of class 1 if G is of class 1 and Δ(H)⩽Δ(G).