### Abstract

Let 1≤a<b be integers and G a Hamiltonian graph of order |G|≥(a+b)(2a+b)/b. Suppose that δ(G)≥a+2 and max{deg _{G}(x),deg_{G}(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.

Original language | English |
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Pages (from-to) | 241-250 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 280 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2004 Apr 6 |

Externally published | Yes |

### Fingerprint

### Keywords

- Connected factor
- Degree condition
- Factor
- Hamiltonian graph

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle.** / Matsuda, Haruhide.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 280, no. 1-3, pp. 241-250. https://doi.org/10.1016/j.disc.2003.10.015

}

TY - JOUR

T1 - Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle

AU - Matsuda, Haruhide

PY - 2004/4/6

Y1 - 2004/4/6

N2 - Let 1≤aG(x),degG(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.

AB - Let 1≤aG(x),degG(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.

KW - Connected factor

KW - Degree condition

KW - Factor

KW - Hamiltonian graph

UR - http://www.scopus.com/inward/record.url?scp=1642406653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1642406653&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2003.10.015

DO - 10.1016/j.disc.2003.10.015

M3 - Article

AN - SCOPUS:1642406653

VL - 280

SP - 241

EP - 250

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -