The Erd\H{o}s, Gr\"unwald and Weiszfeld theorem provides a characterization of infinite graphs which are Eulerian. That is, infinite graphs which admit infinite Eulerian trails. In this article we complement this theorem with a characterization of those finite trails that can be extended to infinite Eulerian trails. This allows us to prove an effective version of the Erd\H{o}s, Gr\"unwald and Weiszfeld theorem for a class of graphs that includes non locally finite ones, generalizing a theorem of D.Bean.

翻译：Erdős、Grünwald和Weiszfeld定理给出了欧拉无限图的刻画。即，那些允许无限欧拉迹的无限图。本文对该定理进行补充，刻画了哪些有限迹可扩展为无限欧拉迹。据此，我们对一类包含非局部有限图在内的图类证明了Erdős、Grünwald和Weiszfeld定理的有效版本，推广了D.Bean的一个定理。