Geodesic
On partitioning the edges of an infinite digraph into directed cycles
Advances in Combinatronics (2021)

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Nash-Williams proved that for an undirected graph $ G $ the set $ E(G) $ can be partitioned into cycles if and only if every cut has either even or infinite number of edges. Later C. Thomassen gave a simpler proof for this 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.
Publié le : 
@article{ADVC_2021_a7,
     author = {Attila Jo\'o},
     title = {On partitioning the edges of an infinite digraph into directed cycles},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a7/}
}
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Attila Joó. On partitioning the edges of an infinite digraph into directed cycles. Advances in Combinatronics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a7/