# On circuits and pancyclic line graphs

Benhocine, A. and Clark, L. and Köhler, N. and Veldman, H.J. (1986) *On circuits and pancyclic line graphs.* Journal of Graph Theory, 10 (3). pp. 411-425. ISSN 0364-9024

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Abstract: | Clark proved that L(G) is hamiltonian if G is a connected graph of order n ≥ 6 such that deg u + deg v ≥ n - 1 - p(n) for every edge uv of G, where p(n) = 0 if n is even and p(n) = 1 if n is odd. Here it is shown that the bound n - 1 - p(n) can be decreased to (2n + 1)/3 if every bridge of G is incident with a vertex of degree 1, which is a necessary condition for hamiltonicity of L(G). Moreover, the conclusion that L(G) is hamiltonian can be strengthened to the conclusion that L(G) is pancyclic. Lesniak-Foster and Williamson proved that G contains a spanning closed trail if |V(G)| = n ≥ 6, δ(G) 2 and deg u + deg v ≥ n - 1 for every pair of nonadjacent vertices u and v. The bound n - 1 can be decreased to (2n + 3)/3 if G is connected and bridgeless, which is necessary for G to have a spanning closed trail. |

Item Type: | Article |

Copyright: | © 1986 Wiley InterScience |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/70813 |

Official URL: | http://dx.doi.org/10.1002/jgt.3190100317 |

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