@article{330494d669214c7c92d02ce48933628b,
title = "A note on minimum degree conditions for supereulerian graphs",
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.",
keywords = "Supereulerian graph, Spanning circuit, Collapsible graph, Degree conditions",
author = "H.J. Broersma and Liming Xiong",
year = "2002",
doi = "10.1016/S0166-218X(01)00278-5",
language = "English",
volume = "120",
pages = "35--43",
journal = "Discrete applied mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "1-3",
}