On Partitioning the Edges of an Infinite Digraph into Directed Cycles
Attila Joó · Advances in Combinatorics · 2021
Nash-Williams proved in [1] that for an undirected graph G the set E¹Gº can be partitioned into cycles if and only if there is no finite cut of odd size. Later C. Thomassen gave a simpler proof for this in [2] and conjectured the following directed analogue of the theorem: the edge set of a digraph can be partitioned into directed cycles if and only if for each subset of the vertices the cardinality of the ingoing and the outgoing edges are equal. The aim of the paper is to prove this conjecture.