Linear k-arboricities on trees

For a xed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number ‘ such that the edge set E(G) can be partitioned into ‘ disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)6m. ? 2000 Elsevier Science B.V. All rights reserved.

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