### Abstract

A graph G is ℓ-hamiltonian if each linear forest F with ℓ edges contained in G can be extended to a hamiltonian cycle of G. We give a sharp upper bound for the maximum number of cliques of a fixed size in a non-ℓ-hamiltonian graph. Furthermore, we prove stability: if a non-ℓ-hamiltonian graph contains almost the maximum number of cliques, then it is a subgraph of one of two extremal graphs.

Original language | English |
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Pages (from-to) | 1919-1923 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 342 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2019 |

### Keywords

- Extremal graph theory
- Hamiltonian cycles
- Turán problem

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Füredi, Z., Kostochka, A., & Luo, R. (2019). A variation of a theorem by Pósa.

*Discrete Mathematics*,*342*(7), 1919-1923. https://doi.org/10.1016/j.disc.2019.03.008