A note on the linear 2-arboricity of planar graphs

作者:Wang, Yiqiao*; Hu, Xiaoxue; Wang, Weifan
来源:Discrete Mathematics, 2017, 340(7): 1449-1455.
DOI:10.1016/j.disc.2017.01.027

摘要

The linear 2-arboricity la(2)(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose components are paths of length at most 2. In this paper, we prove that every planar graph G with Delta = 10 has la(2)(G) <= 9. Using this result, we correct an error in the proof of a result in Wang (2016), which says that every planar graph G satisfies la(2)(G) <= [(Delta+1)/2] + 6.