@book{1840d509b08146f78c3c8a8c73437a6c,

title = "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 $E \subseteq E (G)$ 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.",

keywords = "EWI-3327, MSC-05C45, MSC-05C35, IR-65695",

author = "Broersma, {Haitze J.} and L. Xiong",

note = "Imported from MEMORANDA",

year = "1999",

language = "Undefined",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1507",

}