Covering Planar Graphs with Forests, one Having Bounded Maximum Degree

Abstract : We prove that every planar graph has an edge partition into three forests, one having maximum degree at most 4. This answers a conjecture of Balogh et al. (J. Combin. Theory B. 94 (2005) 147-158). We also prove that every planar graph with girth g > 5 (resp. g > 6) has an edge partition into two forests, one having maximum degree 4 (resp. 2).