Linear arboricity

Linear arboricity is a concept from graph theory that pertains to the decomposition of a graph into linear forests. A linear forest is a disjoint union of paths (which are graphs where each pair of vertices is connected by exactly one simple path) and isolated vertices. The linear arboricity of a graph \( G \), denoted as \( la(G) \), is defined as the minimum number of linear forests into which the edges of the graph can be decomposed.