The Linear 2-Arboricity Of Planar Graphs With Cycle Conditions

Let G(V,E) be a planar graph with maximum degree Δ(G). The linear 2-arboricity of 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.The linear 2-arboricity of planar graphs with cycle conditions are studied in this paper. Main results are described as follow:(1) Let G be a planar graph without 4-and 5-cycles or without 4-and 6-cycles, then(2) Let G be a planar graph without adjacent 4-cycles, then...