Bounded degree acyclic decompositions of digraphs.(English)Zbl 1033.05087

Summary: An acyclic decomposition of a digraph is a partition of the edges into acyclic subgraphs. Trivially every digraph has an acyclic decomposition into two subgraphs. It is proved that for every integer $$s \geqslant 2$$ every digraph has an acyclic decomposition into $$s$$ subgraphs such that in each subgraph the outdegree of each vertex $$v$$ is at most $$\left\lceil \frac {\text{deg}(v)}{s-1} \right\rceil$$. For all digraphs this degree bound is optimal.

MSC:

 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C20 Directed graphs (digraphs), tournaments
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