### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 399-407 |

Journal | Journal of graph theory |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1987 |

### Keywords

- IR-70828

### Cite this

*Journal of graph theory*,

*11*(3), 399-407. https://doi.org/10.1002/jgt.3190110314

}

*Journal of graph theory*, vol. 11, no. 3, pp. 399-407. https://doi.org/10.1002/jgt.3190110314

**3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian.** / Broersma, Haitze J.; Veldman, H.J.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - 3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian

AU - Broersma, Haitze J.

AU - Veldman, H.J.

PY - 1987

Y1 - 1987

N2 - A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.

AB - A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.

KW - IR-70828

U2 - 10.1002/jgt.3190110314

DO - 10.1002/jgt.3190110314

M3 - Article

VL - 11

SP - 399

EP - 407

JO - Journal of graph theory

JF - Journal of graph theory

SN - 0364-9024

IS - 3

ER -