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An upper bound on the linear 2-arboricity of planar graph

XU Chang-qing1, AN Li-sha1, DU Ya-tao2   

  1. 1. Department of Applied Mathematics, Hebei University of Technology, Tianjin 300401, China;
    2. Department of Basic Courses, Ordnance Engineering College, Shijiazhuang 050003, Hebei, China
  • Received:2013-06-18 Online:2014-04-20 Published:2014-06-03

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Abstract: Let G be a planar graph with maximum degree Δ.  The linear 2-arboricity 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. It is denoted by la2(G). We get that la2(G)≤「Δ／2-+8 if Δ≡0,3(mod 4) and la2(G)≤「Δ／2-+7 if Δ≡1,2(mod 4).

Key words: linear arboricity, planar graph, linear 2-arboricity

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