Degree Constrained Orientations in Countable Graphs - Bernáth, Attila; Bruhn, Henning (The Electronic Journal of Combinatorics, 2008)
Degree constrained orientations are orientations of an (undirected) graph where the in-degree function satisfies given lower and upper bounds. For finite graphs Frank and Gyárfás (1976) gave a necessary and sufficient condition for the existence of such an orientation. We extend their result to countable graphs.