### Abstract

We propose the following conjecture to generalize results of Pósa and of Corrádi and Hajnal. Let r, s be nonnegative integers and let G be a graph with | V (G) | ≥ 3 r + 4 s and minimal degree δ (G) ≥ 2 r + 3 s. Then G contains a collection of r + s vertex disjoint cycles, s of them with a chord. We prove the conjecture for r = 0, s = 2 and for s = 1. The corresponding extremal problem, to find the minimum number of edges in a graph on n vertices ensuring the existence of two vertex disjoint chorded cycles, is also settled.

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

Pages (from-to) | 5886-5890 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 23 |

DOIs | |

Publication status | Published - Dec 6 2008 |

### Fingerprint

### Keywords

- Cycles
- Cycles with chords

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*308*(23), 5886-5890. https://doi.org/10.1016/j.disc.2007.10.040

**Disjoint chorded cycles in graphs.** / Bialostocki, Arie; Finkel, Daniel; Gyárfás, A.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 308, no. 23, pp. 5886-5890. https://doi.org/10.1016/j.disc.2007.10.040

}

TY - JOUR

T1 - Disjoint chorded cycles in graphs

AU - Bialostocki, Arie

AU - Finkel, Daniel

AU - Gyárfás, A.

PY - 2008/12/6

Y1 - 2008/12/6

N2 - We propose the following conjecture to generalize results of Pósa and of Corrádi and Hajnal. Let r, s be nonnegative integers and let G be a graph with | V (G) | ≥ 3 r + 4 s and minimal degree δ (G) ≥ 2 r + 3 s. Then G contains a collection of r + s vertex disjoint cycles, s of them with a chord. We prove the conjecture for r = 0, s = 2 and for s = 1. The corresponding extremal problem, to find the minimum number of edges in a graph on n vertices ensuring the existence of two vertex disjoint chorded cycles, is also settled.

AB - We propose the following conjecture to generalize results of Pósa and of Corrádi and Hajnal. Let r, s be nonnegative integers and let G be a graph with | V (G) | ≥ 3 r + 4 s and minimal degree δ (G) ≥ 2 r + 3 s. Then G contains a collection of r + s vertex disjoint cycles, s of them with a chord. We prove the conjecture for r = 0, s = 2 and for s = 1. The corresponding extremal problem, to find the minimum number of edges in a graph on n vertices ensuring the existence of two vertex disjoint chorded cycles, is also settled.

KW - Cycles

KW - Cycles with chords

UR - http://www.scopus.com/inward/record.url?scp=53049088451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53049088451&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2007.10.040

DO - 10.1016/j.disc.2007.10.040

M3 - Article

AN - SCOPUS:53049088451

VL - 308

SP - 5886

EP - 5890

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 23

ER -