### Abstract

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 |

### Fingerprint

### Keywords

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

### Cite this

*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.

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

**Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path.** / Xiong, L.; Broersma, H.J.; Hoede, C.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path

AU - Xiong, L.

AU - Broersma, H.J.

AU - Hoede, C.

N1 - Imported from MEMORANDA

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - MSC-05C45

KW - IR-65793

KW - EWI-3426

KW - MSC-05C35

M3 - Report

T3 - Memorandum

BT - Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -