### Abstract

A graph is called supereulerian if it has a spanning closed trail. Let G be a 2-edge-connected graph of order n such that each minimal edge cut SE(G) with |S|3 satisfies the property that each component of G−S has order at least (n−2)/5. We prove that either G is supereulerian or G belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore, our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree δ4: If G is a 2-edge-connected graph of order n with δ(G)4 such that for every edge xyE(G) , we have max{d(x),d(y)}(n−2)/5−1, then either G is supereulerian or G belongs to one of two classes of exceptional graphs. We show that the condition δ(G)4 cannot be relaxed.

Original language | English |
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Pages (from-to) | 35-43 |

Number of pages | 9 |

Journal | Discrete applied mathematics |

Volume | 120 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2002 |

### Keywords

- Supereulerian graph
- Spanning circuit
- Collapsible graph
- Degree conditions

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## Cite this

Broersma, H. J., & Xiong, L. (2002). A note on minimum degree conditions for supereulerian graphs.

*Discrete applied mathematics*,*120*(1-3), 35-43. https://doi.org/10.1016/S0166-218X(01)00278-5