中文摘要：

如果图G有一个生成的欧拉子图，则称G是超欧拉图．用α（G）表示G中最大独立的边的数目．本文证明了：若G是一个2-边连通简单图且α’（G）≤2，则G要么是可折叠图，要么存在G的某个连通子图H，使得对某个正整数t≥2，约化图G／H是K2,t．推广了[Lai H J，Yan H.Supereulerian graphs and matchings．Appl．Math．Lett．，2011，24：1867-1869]中的一个主要结果．并且证明了上述文献中提出的一个猜想：3-边连通且α’（G）≤5的简单图是超欧拉图当且仅当它不可收缩成Petersen图．

英文摘要：

A graph G is called supereulerian if G has a spanning eulerian subgraph. Let ar （G） be the maximum number of independent edges in the graph G. In this paper we show that if G is a 2-edge-connected simple graph and α＇/（G） ≤2, then either G is collapsible, or there is a connected subgraph H of G such that the contraction G/H is K2,t for some positive integer t≥ 2. This strengthens the main result of [Lai H J, Yan H. Supereulerian graphs and matchings. Appl. Math. Lett., 2011, 24： 1867-1869]. We also verify a conjecture in the same paper above, that if G is a 3-edge-connected simple graph and α＇（G） 〈 5, then G is supereulerian if and only if G is not contractible to the Petersen graph.