### Abstract

Let S be a set of vertices of a k-connected graph G. We denote the smallest sum of degrees of k + 1 independent vertices of S by σ_{k + 1}(S; G). We obtain a sharp lower bound of σ_{k + 1}(S; G) for the vertices of S to be contained in a common cycle of G. This result gives a sufficient condition for a k-connected graph to be hamiltonian.

Original language | English |
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Pages (from-to) | 201-210 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 145 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1995 Oct 13 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*145*(1-3), 201-210. https://doi.org/10.1016/0012-365X(94)00036-I

**Cycles through prescribed vertices with large degree sum.** / Ota, Katsuhiro.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 145, no. 1-3, pp. 201-210. https://doi.org/10.1016/0012-365X(94)00036-I

}

TY - JOUR

T1 - Cycles through prescribed vertices with large degree sum

AU - Ota, Katsuhiro

PY - 1995/10/13

Y1 - 1995/10/13

N2 - Let S be a set of vertices of a k-connected graph G. We denote the smallest sum of degrees of k + 1 independent vertices of S by σk + 1(S; G). We obtain a sharp lower bound of σk + 1(S; G) for the vertices of S to be contained in a common cycle of G. This result gives a sufficient condition for a k-connected graph to be hamiltonian.

AB - Let S be a set of vertices of a k-connected graph G. We denote the smallest sum of degrees of k + 1 independent vertices of S by σk + 1(S; G). We obtain a sharp lower bound of σk + 1(S; G) for the vertices of S to be contained in a common cycle of G. This result gives a sufficient condition for a k-connected graph to be hamiltonian.

UR - http://www.scopus.com/inward/record.url?scp=0038282286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038282286&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(94)00036-I

DO - 10.1016/0012-365X(94)00036-I

M3 - Article

AN - SCOPUS:0038282286

VL - 145

SP - 201

EP - 210

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -