On the Linear 2-Arboricity of Planar Graphs without Intersecting 3-Cycles or Intersecting 4-Cycles

The linear 2-arboricity la(2)(G) of a graph G is the least integer k such that G can be partitioned into k edge disjoint forests, whose component trees are paths of length at most 2. Two cycles are intersecting if they have at least one common vertex. Let G be a simple planar graph with maximum degree Delta. We prove that la(2)(G) <= inverted right perpendicular Delta/2inverted left perpendicular +6 if G has no intersecting 3-cycles or no intersecting 4-cycles.