On the linear 2-arboricity of planar graph without normally adjacent 3-cycles and 4-cycles
Yiqiao Wang · International Journal of Computer Mathematics · 2016
The linear 2-arboricity la2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose components are paths of length at most 2. In this paper, we prove that if G is a planar graph in which there do not exist a 3-cycle and a 4-cycle sharing exactly one common edge, then la2(G)≤⌈Δ(G)/2⌉+5. This improves some currently known results.