### Abstract

The k-linear arboricity of a graph G is the minimum number of forests whose connected components are paths of length at most k which partition E(G). Motivated by this index, we investigate a variation of this idea for d-regular graphs. Namely, we define a d-regular graph G to be (l, k)-linear arborific if E(G) can be partitioned into edge sets of l linear forests consisting of paths of length at most k. By extending an inductive tool developed by Jackson and Wormald, we determine, for d ≥ 4, values of k such that every d-regular graph is (d - l, k)-linear arborific.

Original language | English |
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Pages (from-to) | 217-226 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 186 |

Issue number | 1-3 |

Publication status | Published - 15 May 1998 |

Externally published | Yes |

## Cite this

Lindquester, T., & Wormald, N. C. (1998). Factorisation of regular graphs into forests of short paths.

*Discrete Mathematics*,*186*(1-3), 217-226.