Infinite Eulerian paths are computable on graphs with vertices of infinite degree

Abstract: The Erd\H{o}s, Gr\"unwald, and Weiszfeld theorem is a characterization of those infinite graphs which are Eulerian. That is, infinite graphs that admit infinite Eulerian paths. In this article we prove an effective version of the Erd\H{o}s, Gr\"unwald, and Weiszfeld theorem for a class of graphs where vertices of infinite degree are allowed, generalizing a theorem of D.Bean. Our results are obtained from a characterization of those finite paths in a graph that can be extended to infinite Eulerian paths.