### Nowhere-zero 5-flows and (1, 2)-factors

### Abstract

A graph G has a nowhere-zero k-flow if there exists an orientation D of the edges and an integer flow Ï†{symbol} such that for all e âˆˆ D (G), 0 < | Ï†{symbol} (e) | < k. A (1, 2)-factor is a subset of the edges F âŠ† E (G) such that the degree of any vertex in the subgraph induced by F is 1 or 2. It is known that cubic graphs having a nowhere-zero k-flow with k = 3, 4 are characterized by properties of the cycles of the graph. We extend these results by giving a characterization of cubic graphs having a nowhere-zero 5-flow based on the existence of a (1, 2)-factor of the graph such that the cycles of the graph satisfies an algebraic property. Â© 2008 Elsevier B.V. All rights reserved.

### Más información

Título según SCOPUS: | Nowhere-zero 5-flows and (1, 2)-factors |

Título de la Revista: | Electronic Notes in Discrete Mathematics |

Volumen: | 30 |

Número: | C |

Editorial: | Elsevier |

Fecha de publicación: | 2008 |

Página de inicio: | 279 |

Página final: | 284 |

Idioma: | eng |

URL: | http://www.scopus.com/inward/record.url?eid=2-s2.0-39149092663&partnerID=q2rCbXpz |

DOI: |
10.1016/j.endm.2008.01.048 |

Notas: | SCOPUS |