### Abstract

Bollobás and Thomason showed that a multigraph of order n and size at least n + c (c ≥ 1) contains a cycle of length at most 2(⌊n/c⌋ + 1) ⌊log2 2c⌋. We show in this paper that a multigraph (with no loop) of order n and minimum degree at least 5 contains a chorded cycle (a cycle with a chord) of length at most 300 log2 n. As an application of this result, we show that a graph of sufficiently large order with minimum degree at least 3k+8 contains k vertex-disjoint chorded cycles of the same length, which is analogous to Verstraëte's result: A graph of sufficiently large order with minimum degree at least 2k contains k vertex-disjoint cycles of the same length.

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

Pages (from-to) | 1030-1041 |

Number of pages | 12 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

- Chorded cycles
- Cycles
- Minimum degree

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*SIAM Journal on Discrete Mathematics*,

*29*(2), 1030-1041. https://doi.org/10.1137/130929837

**Disjoint chorded cycles of the same length.** / Chen, Guantao; Gould, Ronald J.; Hirohata, Kazuhide; Ota, Katsuhiro; Shan, Songling.

Research output: Contribution to journal › Article

*SIAM Journal on Discrete Mathematics*, vol. 29, no. 2, pp. 1030-1041. https://doi.org/10.1137/130929837

}

TY - JOUR

T1 - Disjoint chorded cycles of the same length

AU - Chen, Guantao

AU - Gould, Ronald J.

AU - Hirohata, Kazuhide

AU - Ota, Katsuhiro

AU - Shan, Songling

PY - 2015

Y1 - 2015

N2 - Bollobás and Thomason showed that a multigraph of order n and size at least n + c (c ≥ 1) contains a cycle of length at most 2(⌊n/c⌋ + 1) ⌊log2 2c⌋. We show in this paper that a multigraph (with no loop) of order n and minimum degree at least 5 contains a chorded cycle (a cycle with a chord) of length at most 300 log2 n. As an application of this result, we show that a graph of sufficiently large order with minimum degree at least 3k+8 contains k vertex-disjoint chorded cycles of the same length, which is analogous to Verstraëte's result: A graph of sufficiently large order with minimum degree at least 2k contains k vertex-disjoint cycles of the same length.

AB - Bollobás and Thomason showed that a multigraph of order n and size at least n + c (c ≥ 1) contains a cycle of length at most 2(⌊n/c⌋ + 1) ⌊log2 2c⌋. We show in this paper that a multigraph (with no loop) of order n and minimum degree at least 5 contains a chorded cycle (a cycle with a chord) of length at most 300 log2 n. As an application of this result, we show that a graph of sufficiently large order with minimum degree at least 3k+8 contains k vertex-disjoint chorded cycles of the same length, which is analogous to Verstraëte's result: A graph of sufficiently large order with minimum degree at least 2k contains k vertex-disjoint cycles of the same length.

KW - Chorded cycles

KW - Cycles

KW - Minimum degree

UR - http://www.scopus.com/inward/record.url?scp=84938094076&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938094076&partnerID=8YFLogxK

U2 - 10.1137/130929837

DO - 10.1137/130929837

M3 - Article

AN - SCOPUS:84938094076

VL - 29

SP - 1030

EP - 1041

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -