【摘要】 P.A.Catlin提出一个问题:设H是图G的一个连通子图,如果G关于H的收缩图G/H有一个欧拉生成子图,那么在什么条件下G也有一个欧拉生成子图?研究了这一问题,讨论了Catlin提出的用收缩法判定超欧拉图的两个定理,给出了一些实用的超欧拉图的判别方法.更多还原

【Abstract】 P. A. Catlin posed a question: Let G be a graph, and let H be a connected subgraph of G. When it is known that the graph G/H(obtained from G by contracting H to a vertex)has a spanning Eulerian subgraph, under what conditions can it be inferred that G itself has a spanning Eulerian subgraph? [J. Graph Theory,22 (1996) , 152 -153]. In the paper, we discuss two theorems that Catlin made to decide whether a graph is supereulerian. In addition some practical methods to determine if a graph is supereulerian are presented.更多还原