### Abstract

A (d, k) -forest is a forest consisting of trees whose diameters are at most d and whose maximum vertex degree,Δ is at most k. The (d, k)-arboricity of a graph G is the minimum number of (d, k)-forests needed to cover E(G). This concept is a common generalization of linear k-arboricity and star arboricity. Using a probabilistic approach developed recently for linear karboricity, we obtain an upper bound on the (d, k)-arboricity of r-regular graphs.

Original language | English |
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Pages (from-to) | 219-226 |

Number of pages | 8 |

Journal | Australasian Journal of Combinatorics |

Volume | 22 |

Publication status | Published - 2000 |

Externally published | Yes |

## Cite this

Assiyatun, H., & Wormald, N. C. (2000). Covering regular graphs with forests of small trees.

*Australasian Journal of Combinatorics*,*22*, 219-226.