The Linear $2$-Arboricity of Some Planar Graphs

Abstract

Let $G$ be a planar graph with maximum degree $\mathrm{\Delta }(G)$. The least integer $k$ such that $G$ can be partitioned into $k$ edge-disjoint forests, where each component is a path of length at most $2$, is called the linear $2$-arboricity of $G$, denoted by $l{a}_2(G)$. We establish new upper bounds for the linear $2$-arboricity of certain planar graphs.