## Abstract

For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In (J Graph Theory 11:399-407 (1987)), Broersma and Veldman proposed an open problem: for a given positive integer k, determine the value s for which the statement "Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected" is valid. Broersma and Veldman proved in 1987 that the statement above holds for 0 ≤ s ≤ k and asked, specifically, if the statement holds when s = 2k. In this paper, we prove that the statement above holds for 0 ≤ s ≤ max{2k, 6k - 16}.

Original language | English |
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Pages (from-to) | 241-248 |

Number of pages | 8 |

Journal | Graphs and Combinatorics |

Volume | 23 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 2007 |

## Scopus Subject Areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics