The linear 2-arboricity of sparse graphs
Yuanchao Li, Xiaoxue Hu · Discrete Mathematics Algorithms and Applications · 2017
The linear [Formula: see text]-arboricity [Formula: see text] of a graph [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] can be partitioned into [Formula: see text] edge-disjoint forests, whose components are paths of length at most 2. In this paper, we study the linear [Formula: see text]-arboricity of sparse graphs, and prove the following results: (1) let [Formula: see text] be a 2-degenerate graph, we have [Formula: see text]; (2) if [Formula: see text], then [Formula: see text]; (3) if [Formula: see text], then [Formula: see text]; (4) if [Formula: see text], then [Formula: see text]; (5) if [Formula: see text], then [Formula: see text].