### Abstract

A graph is called {\sl subpancyclic} if it contains a cycle of length $l$ for each $l$ between 3 and the circumference of a graph. We show that if $G$ is a connected graph on $n\geq 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>\frac{n+10}{2}$ for all four $u, v, x, y$ of a path $P=uvxy$ in $G, $ then its line graph is subpancyclic unless $G$ is isomorphic to an exceptional graph, and the result is best possible, even under the condition that $L(G)$ is hamiltonian.

Original language | English |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 13 |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1606 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C45
- IR-65793
- EWI-3426
- MSC-05C35

## Fingerprint Dive into the research topics of 'Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path'. Together they form a unique fingerprint.

## Cite this

Xiong, L., Broersma, H. J., & Hoede, C. (2001).

*Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path*. (Memorandum; No. 1606). Enschede: University of Twente, Department of Applied Mathematics.