### Abstract

For c≥2 and k≤min{c,3}, guaranteed upper bounds on the length of a shortest cycle through k prescribed vertices of a c-connected graphs were proved. Analogous results on planar graphs were also presented. A version of Menger's theorem and a structural lemma for c-connected graphs were proved. The upper bounds by constructing graphs having no cycles shorter than l containing the prescribed set of vertices and lower bounds by detecting large unavoidable substructures were established.

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

Pages (from-to) | 67-74 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 286 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Sep 6 2004 |

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### Keywords

- Graph
- Prescribed vertices
- Short cycle

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*286*(1-2), 67-74. https://doi.org/10.1016/j.disc.2003.11.047

**On short cycles through prescribed vertices of a graph.** / Göring, F.; Harant, J.; Hexel, E.; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 286, no. 1-2, pp. 67-74. https://doi.org/10.1016/j.disc.2003.11.047

}

TY - JOUR

T1 - On short cycles through prescribed vertices of a graph

AU - Göring, F.

AU - Harant, J.

AU - Hexel, E.

AU - Tuza, Z.

PY - 2004/9/6

Y1 - 2004/9/6

N2 - For c≥2 and k≤min{c,3}, guaranteed upper bounds on the length of a shortest cycle through k prescribed vertices of a c-connected graphs were proved. Analogous results on planar graphs were also presented. A version of Menger's theorem and a structural lemma for c-connected graphs were proved. The upper bounds by constructing graphs having no cycles shorter than l containing the prescribed set of vertices and lower bounds by detecting large unavoidable substructures were established.

AB - For c≥2 and k≤min{c,3}, guaranteed upper bounds on the length of a shortest cycle through k prescribed vertices of a c-connected graphs were proved. Analogous results on planar graphs were also presented. A version of Menger's theorem and a structural lemma for c-connected graphs were proved. The upper bounds by constructing graphs having no cycles shorter than l containing the prescribed set of vertices and lower bounds by detecting large unavoidable substructures were established.

KW - Graph

KW - Prescribed vertices

KW - Short cycle

UR - http://www.scopus.com/inward/record.url?scp=4344599583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344599583&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2003.11.047

DO - 10.1016/j.disc.2003.11.047

M3 - Article

AN - SCOPUS:4344599583

VL - 286

SP - 67

EP - 74

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-2

ER -