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

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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.
Item Type:	Article
Copyright:	© 2002 Elsevier
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/74789
Official URL:	http://dx.doi.org/10.1016/S0166-218X(01)00278-5
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