The linear arboricity of planar graphs with maximum degree at least 7

Abstract

The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. In this paper,it is proved that for two fixed integers i and j(3 ≤ i ≤ j ≤ 5),if a planar graph G has the maximum degree at least 7 and any two cycles of length i and j,respectively,are not adjacent,then its linear arboricity is [Δ(G)/2].