The Linear \(2\)-Arboricity of Some Planar Graphs

Abstract

Let \(G\) be a planar graph with maximum degree \(\Delta(G)\). 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 \(la_2(G)\). We establish new upper bounds for the linear \(2\)-arboricity of certain planar graphs.