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THE LINEAR 2-ARBORICITY OF PLANAR GRAPHS WITH MAXIMUM DEGREE 9
Xiaoxue Hu,Jiangxu Kong,Yiqiao Wang
Keywords:Plane graph, linear 2-arboricity, maximum degree
Abstract:
      The linear 2-arboricity la 2 (G) of 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. In 2017, wang et al. proved that every planar graph G with ?(G) ≥ 10 has la 2 (G) ≤ ?(G)?1. The condition ? ≥ 10 is improved to ? ≥ 9 in this paper.