### Abstract

A sequence d = (d_{1}, d_{2}, ..., d_{n}) is graphic if there is a simple graph G with degree sequence d, and such a graph G is called a realization of d. A graphic sequence d is line-hamiltonian if d has a realization G such that L (G) is hamiltonian, and is supereulerian if d has a realization G with a spanning eulerian subgraph. In this paper, it is proved that a nonincreasing graphic sequence d = (d_{1}, d_{2}, ..., d_{n}) has a supereulerian realization if and only if d_{n} ≥ 2 and that d is line-hamiltonian if and only if either d_{1} = n - 1, or ∑_{di = 1} d_{i} ≤ ∑_{dj ≥ 2} (d_{j} - 2).

Original language | English (US) |
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Pages (from-to) | 6626-6631 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 24 |

DOIs | |

State | Published - Dec 28 2008 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Fan, S., Lai, H. J., Shao, Y., Zhang, T., & Zhou, J. (2008). Degree sequence and supereulerian graphs.

*Discrete Mathematics*,*308*(24), 6626-6631. https://doi.org/10.1016/j.disc.2007.11.008