### Abstract

A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n+6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n+16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy.

Original language | English |
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Pages (from-to) | 255-267 |

Number of pages | 13 |

Journal | Discrete mathematics |

Volume | 242 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2002 |

### Keywords

- Line graph
- Path
- Subpancyclicity
- IR-74722
- Degree sum
- METIS-206788

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## Cite this

Xiong, L., Broersma, H. J., Hoede, C., Li, X., & Li, X. (2002). Degree sums and subpancyclicity in line graphs.

*Discrete mathematics*,*242*(1-3), 255-267. https://doi.org/10.1016/S0012-365X(00)00468-4