The linear arboricity of planar graphs without adjacent 4-cycles

Abstract

Let G be a planar graph with maximum degree Δ ≥ 5 and without adjacent 4-cycles. In this paper, it is proved that la(G)= [Δ/2] if a 3-cycle and a 5-cycle are not adjacent in G, or a 3-cycle and a 4-cycle are not intersecting in G.