On the Anderson–Lipman conjecture and some related problems

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