On Partitioning the Edges of an Infinite Digraph into Directed Cycles

Nash-Williams proved in [1] that for an undirected graph G the set E¹Gº can be partitioned into cycles if and only there is no finite cut of odd size. Later C. Thomassen gave a simpler proof this [2] conjectured following directed analogue theorem: edge digraph each subset vertices cardinality ingoing outgoing edges are equal. The aim paper to prove conjecture.