Decomposition of 8-regular graphs into paths of length 4

A Pℓ-decomposition of a graph G is a set of edge-disjoint copies of Pℓ in G that cover the edge set of G, where Pℓ is the path with ℓ edges. Kouider and Lonc [M. Kouider, Z. Lonc, Path decompositions and perfect path double covers, Australas. J. Combin. 19 (1999) 261-274] conjectured that any 2ℓ-regular graph G admits a Pℓ-decomposition D where every vertex of G is the end-vertex of exactly two paths of D. In this paper we verify Kouider and Lonc's Conjecture for paths of length 4.