### Abstract

Let k ≥ 2 be an integer and G a 2-connected graph of order {pipe}G{pipe} ≥ 3 with minimum degree at least k. Suppose that {pipe}G{pipe} ≥ 8k - 16 for even {pipe}G{pipe} and {pipe}G{pipe} ≥ 6k - 13 for odd {pipe}G{pipe}. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{deg_{G}(x), deg_{G}(y)} ≥ {pipe}G{pipe}/2 for each pair of nonadjacent vertices x and y in G. This is best possible in the sense that there exists a graph having no k-factor containing a given Hamiltonian cycle under the same conditions. The lower bound of {pipe}G{pipe} is also sharp.

Original language | English |
---|---|

Pages (from-to) | 273-281 |

Number of pages | 9 |

Journal | Australasian Journal of Combinatorics |

Volume | 26 |

Publication status | Published - 2002 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

**Degree conditions for the existence of [k, k + 1]-factors containing a given Hamiltonian cycle.** / Matsuda, Haruhide.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Degree conditions for the existence of [k, k + 1]-factors containing a given Hamiltonian cycle

AU - Matsuda, Haruhide

PY - 2002

Y1 - 2002

N2 - Let k ≥ 2 be an integer and G a 2-connected graph of order {pipe}G{pipe} ≥ 3 with minimum degree at least k. Suppose that {pipe}G{pipe} ≥ 8k - 16 for even {pipe}G{pipe} and {pipe}G{pipe} ≥ 6k - 13 for odd {pipe}G{pipe}. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{degG(x), degG(y)} ≥ {pipe}G{pipe}/2 for each pair of nonadjacent vertices x and y in G. This is best possible in the sense that there exists a graph having no k-factor containing a given Hamiltonian cycle under the same conditions. The lower bound of {pipe}G{pipe} is also sharp.

AB - Let k ≥ 2 be an integer and G a 2-connected graph of order {pipe}G{pipe} ≥ 3 with minimum degree at least k. Suppose that {pipe}G{pipe} ≥ 8k - 16 for even {pipe}G{pipe} and {pipe}G{pipe} ≥ 6k - 13 for odd {pipe}G{pipe}. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{degG(x), degG(y)} ≥ {pipe}G{pipe}/2 for each pair of nonadjacent vertices x and y in G. This is best possible in the sense that there exists a graph having no k-factor containing a given Hamiltonian cycle under the same conditions. The lower bound of {pipe}G{pipe} is also sharp.

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UR - http://www.scopus.com/inward/citedby.url?scp=1642389779&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1642389779

VL - 26

SP - 273

EP - 281

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

ER -