image-Valuations for some stunted trees

A tree with image edges is stunted if its edges can be linearly ordered image so that image and image share a vertex and, for all image, edge image shares a vertex with at least one edge image satisfying image. Using Alonʹs “Combinatorial Nullstellensatz”, a short proof is given showing that if image is prime, then every stunted tree with image edges has a image-valuation. Consequently, every stunted tree on image edges cyclically decomposes the complete graph image.