Hoffmann-Ostenhof's conjecture for traceable cubic graphs
  It was conjectured by Hoffmann-Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. In this paper, we show that this conjecture holds for traceable cubic graphs. 
F. Abdolhosseini, S. Akbari, H. Hashemi, M.S. Moradian
math.CO cs.DM