### Abstract

The problems related to the partitioning of undirected graphs using undirectional analogues with no loops and no multiple edges was studied. The problem regarding for which values d_{1}≥ d_{2} ≥··· ≥ d_{k} 1, particularly finiteness of F(2,1) was analyzed. It was observed that the vertex set can be partitioned into two parts if the maximum degree is 2d+1. Characterization of all the sequences of integers (Δ, d_{1}, d_{2}, _{}·· _{}·, d_{k}) for the vertex set of any digraph showed that (m+n, ≥ q+r)digraph must contain either an (digraph, ≥q)-digraph, or an (n, ≥)-digraph to be (n, ≥ q)-digraph containing at least q outdegrees.

Original language | English (US) |
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Pages (from-to) | 933-937 |

Number of pages | 5 |

Journal | Combinatorics Probability and Computing |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 2006 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Alon, N. (2006). Splitting digraphs.

*Combinatorics Probability and Computing*,*15*(6), 933-937. https://doi.org/10.1017/S0963548306008042