## Taiwanese Journal of Mathematics

### ALGORITHMIC ASPECTS OF LINEAR k-ARBORICITY

Gerard J. Chang

#### 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 $\rm la_2(T)=m$.

#### Article information

Source
Taiwanese J. Math., Volume 3, Number 1 (1999), 71-81.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407055

Digital Object Identifier
doi:10.11650/twjm/1500407055

Mathematical Reviews number (MathSciNet)
MR1676023

Zentralblatt MATH identifier
0927.05073

#### Citation

Chang, Gerard J. ALGORITHMIC ASPECTS OF LINEAR k-ARBORICITY. Taiwanese J. Math. 3 (1999), no. 1, 71--81. doi:10.11650/twjm/1500407055. https://projecteuclid.org/euclid.twjm/1500407055