The Linear $2$-Arboricity of Outerplanar Graphs

Abstract

The linear $2$-arboricity $l{a}_2(G)$ of a graph $G$ is the least integer $k$ such that $G$ can be partitioned into $k$ edge-disjoint forests, whose component trees are paths of length at most $2$. We prove that $l{a}_2(G)\le \lfloor \frac{\mathrm{\Delta }(G)+4}{2}\rfloor$ if $G$ is an outerplanar graph with maximum degree $\mathrm{\Delta }(G)$.