### Abstract

Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.

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

Title of host publication | Lecture Notes in Computer Science |

Editors | J. Akiyama, E.T. Baskoro, M. Kano |

Pages | 123-132 |

Number of pages | 10 |

Volume | 3330 |

Publication status | Published - 2005 |

Externally published | Yes |

Event | Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003 - Bandung, Indonesia Duration: 2003 Sep 13 → 2003 Sep 16 |

### Other

Other | Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003 |
---|---|

Country | Indonesia |

City | Bandung |

Period | 03/9/13 → 03/9/16 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3330, pp. 123-132)

**Regular factors containing a given hamiltonian cycle.** / Matsuda, Haruhide.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science.*vol. 3330, pp. 123-132, Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003, Bandung, Indonesia, 03/9/13.

}

TY - GEN

T1 - Regular factors containing a given hamiltonian cycle

AU - Matsuda, Haruhide

PY - 2005

Y1 - 2005

N2 - Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.

AB - Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.

UR - http://www.scopus.com/inward/record.url?scp=23944486377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23944486377&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:23944486377

VL - 3330

SP - 123

EP - 132

BT - Lecture Notes in Computer Science

A2 - Akiyama, J.

A2 - Baskoro, E.T.

A2 - Kano, M.

ER -