An improved upper bound on the linear 2-arboricity of planar graphs

The linear 2-arboricity la2(G) of a graph GG is the least integer kk such that GG can be partitioned into kk edge-disjoint forests, whose component trees are paths of length at most 2. In this paper, we prove that if GG is a planar graph, then la2(G)≤⌈(Δ(G)+1)/2⌉+6. This improves a result in Lih et al. (2003), which says that every planar graph GG satisfies la2(G)≤⌈(Δ(G)+1)/2⌉+12.