ALGORITHMIC ASPECTS OF LINEAR k-ARBORICITY

Abstract

For a fixed positive integer $k$, the linear $k$-arboricity $\rm la_k(G)$ of a graph $G$ is the minimum number $\ell$ such that the edge set $E(G)$ can be partitioned into $\ell$ disjoint sets, each induces a subgraph whose components are paths of lengths at most $k$. This paper examines linear $k$-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm for determining whether a tree $T$ has $\rm la_2(T)\le m$. We also give a characterization for a tree $T$ with maximum degree $2m$ having $\rm la_2(T)=m$.