# A note on minimum degree conditions for supereulerian graphs

Broersma, H.J.
and
Xiong, Liming
(2002)
*A note on minimum degree conditions for supereulerian graphs.*
Discrete Applied Mathematics, 120
(1-3).
pp. 35-43.
ISSN 0166-218X

PDF
Restricted to UT campus only : Request a copy 98kB |

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(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. |

Item Type: | Article |

Copyright: | © 2002 Elsevier |

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

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/74789 |

Official URL: | http://dx.doi.org/10.1016/S0166-218X(01)00278-5 |

Export this item as: | BibTeX EndNote HTML Citation Reference Manager |

Repository Staff Only: item control page

Metis ID: 206795