LINEAR 2-ARBORICITY OF PLANAR GRAPHS WITH MAXIMUM DEGREE NINE

Abstract

<abstract> 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 component trees are paths of length at most 2. In this paper, we show that every planar graph $G$ with maximum degree $\Delta=9$ has la$_2(G)\le 8$, which extends a known result that every planar graph $G$ with $\Delta\ge10$ has la$_2(G)\le \Delta-1$. </abstract>