## Abstract

We prove that for all natural numbers

*and***m****where k is odd, there exists a natural number***k***such that any 3-connected cubic graph with at least***N(k)**vertices contains a cycle of length m modulo***N(k)***k*. We also construct a family of graphs showing that this is not true for 2-connected cubic graphs if*and***m****are divisible by 3 and***k***≥12.***k*Original language | English |
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Journal | Advances in Combinatorics |

Number of pages | 36 |

ISSN | 2517-5599 |

DOIs | |

Publication status | Published - 2021 |

## Keywords

- 3-connected
- Cubic graphs
- Cycles