### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 1999 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1507 |

ISSN (Print) | 0169-2690 |

### Keywords

- EWI-3327
- MSC-05C45
- MSC-05C35
- IR-65695

### Cite this

*On minimum degree conditions for supereulerian graphs*. Enschede: University of Twente, Department of Applied Mathematics.

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*On minimum degree conditions for supereulerian graphs*. University of Twente, Department of Applied Mathematics, Enschede.

**On minimum degree conditions for supereulerian graphs.** / Broersma, Haitze J.; Xiong, L.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - On minimum degree conditions for supereulerian graphs

AU - Broersma, Haitze J.

AU - Xiong, L.

N1 - Imported from MEMORANDA

PY - 1999

Y1 - 1999

N2 - 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 $E \subseteq E (G)$ with $|E| \le 3$ satisfies the property that each component of $G-E$ 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 $\delta\ge 4$: If $G$ is a 2-edge-connected graph of order $n$ with $\delta (G)\ge 4$ such that for every edge $xy\in E (G)$ , we have $\max \{d(x),d(y)\} \ge (n-7)/5$, then either $G$ is supereulerian or $G$ belongs to one of two classes of exceptional graphs. We show that the condition $\delta(G)\ge 4$ cannot be relaxed.

AB - 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 $E \subseteq E (G)$ with $|E| \le 3$ satisfies the property that each component of $G-E$ 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 $\delta\ge 4$: If $G$ is a 2-edge-connected graph of order $n$ with $\delta (G)\ge 4$ such that for every edge $xy\in E (G)$ , we have $\max \{d(x),d(y)\} \ge (n-7)/5$, then either $G$ is supereulerian or $G$ belongs to one of two classes of exceptional graphs. We show that the condition $\delta(G)\ge 4$ cannot be relaxed.

KW - EWI-3327

KW - MSC-05C45

KW - MSC-05C35

KW - IR-65695

M3 - Report

BT - On minimum degree conditions for supereulerian graphs

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -