# On minimum degree conditions for supereulerian graphs

Broersma, H.J. and Xiong, L. (1999) On minimum degree conditions for supereulerian graphs. [Report]

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 Abstract: A graph is called supereulerian if it has a spanning closed trail. Let be a 2-edge-connected graph of order such that each minimal edge cut with satisfies the property that each component of has order at least . We prove that either is supereulerian or 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 : If is a 2-edge-connected graph of order with such that for every edge , we have , then either is supereulerian or belongs to one of two classes of exceptional graphs. We show that the condition cannot be relaxed. Item Type: Report Additional information: Imported from MEMORANDA Faculty: Electrical Engineering, Mathematics and Computer Science (EEMCS) Research Group: Link to this item: http://purl.utwente.nl/publications/65695 Export this item as: BibTeXEndNoteHTML CitationReference Manager

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