### Abstract

A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted by la_{k} (G), is the least number of linear k-forests needed to decompose G. In this paper, we completely determine la_{k} (G) when G is a balanced complete bipartite graph K_{n, n} or a complete graph K_{n}, and k = 3.

Original language | English |
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Pages (from-to) | 3816-3823 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 17 |

DOIs | |

State | Published - 6 Sep 2008 |

### Keywords

- Balanced complete bipartite graph
- Complete graph
- Linear k-arboricity
- Linear k-forest

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## Cite this

Fu, H-L., Huang, K. C., & Yen, C. H. (2008). The linear 3-arboricity of Kn, n and Kn.

*Discrete Mathematics*,*308*(17), 3816-3823. https://doi.org/10.1016/j.disc.2007.07.067