The linear arboricity of planar graphs without chordal short cycles

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 if a planar graph G with Δ(G) ≥ 7 and without chordal i-cycles for some i ∈ {4,5,6,7}, then la(G) = [Δ(G)/2]. It generalizes the result in [3], [4] and [10].