In this paper we present a short proof of a theorem by Erd\H{o}s, Gr\"unwald and Weiszfeld on the characterization of infinite graphs which admit infinite Eulerian trails. In addition, we extend this result with a characterization of which finite trails can be extended to infinite Eulerian trails. Our proof is computable and yields an effective version of this theorem. This exhibits stark contrast with other classical results in the theory of infinite graphs which are not effective.

翻译：本文给出了Erdős, Grünwald和Weiszfeld关于可容纳无限欧拉迹的无限图刻画定理的一个简短证明。此外，我们通过刻画哪些有限迹可扩展为无限欧拉迹，对该结果进行了推广。我们的证明是可计算的，并给出了该定理的一个有效版本。这与无限图理论中其他非有效的经典结果形成了鲜明对比。