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

TL;DR

This paper extends the characterization of infinite Eulerian paths to graphs with vertices of infinite degree, providing an effective criterion for their computability.

Contribution

It generalizes the Erd ext{"o}s, Gr"unwald, and Weiszfeld theorem to include graphs with infinite degree vertices, building on D.Bean's work.

Findings

Effective characterization of infinite Eulerian paths in graphs with infinite degree vertices

Extension of classical Eulerian path theorems to more general infinite graphs

Conditions under which finite paths extend to infinite Eulerian paths

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.