### 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 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cycle
- Even factor
- Factor
- Trail
- Walk

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Ore-type conditions for the existence of even [2,b]-factors in graphs.** / Matsuda, Haruhide.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 304, no. 1-3, pp. 51-61. https://doi.org/10.1016/j.disc.2005.09.009

}

TY - JOUR

T1 - Ore-type conditions for the existence of even [2,b]-factors in graphs

AU - Matsuda, Haruhide

PY - 2005/11/28

Y1 - 2005/11/28

N2 - 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.

AB - 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.

KW - Cycle

KW - Even factor

KW - Factor

KW - Trail

KW - Walk

UR - http://www.scopus.com/inward/record.url?scp=27944462759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27944462759&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2005.09.009

DO - 10.1016/j.disc.2005.09.009

M3 - Article

AN - SCOPUS:27944462759

VL - 304

SP - 51

EP - 61

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -