### 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 |
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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 |

### Keywords

- Chorded cycles
- Cycles
- Minimum degree

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*SIAM Journal on Discrete Mathematics*,

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