### Abstract

For even b≥2, an even [2,b]-factor is a spanning subgraph each of whose degree is even between 2 and b. The main result is the following: a 2-edge-connected graph G of order n has an even [2,b]-factor if the degree sum of each pair of nonadjacent vertices in G is at least max⌈4n/(2+b), 5⌉. These lower bounds are best possible in some sense. The condition "2-edge-connected" cannot be dropped. This result was conjectured by Kouider and Vestergaard, and also is related to the study of Hamilton cycles, connected factors, spanning k-walks, and supereulerian graphs. Moreover, a related open problem is posed.

Original language | English |
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Pages (from-to) | 51-61 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 304 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2005 Nov 28 |

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### Keywords

- Cycle
- Even factor
- Factor
- Trail
- Walk

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics