Minimal representation of directed hypergraphs
SIAM Journal on Computing
Directed hypergraphs and applications
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Introduction to the theory of complexity
Introduction to the theory of complexity
Cayley Digraphs Based on the de Bruijn Networks
SIAM Journal on Discrete Mathematics
Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
On the orientation of graphs and hypergraphs
Discrete Applied Mathematics - Submodularity
The complexity of arc-colorings for directed hypergraphs
Discrete Applied Mathematics
The complexity of arc-colorings for directed hypergraphs
Discrete Applied Mathematics
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We address some complexity questions related to the arc-coloring of directed hypergraphs. Such hypergraphs arise as a generalization of digraphs, by allowing the tail of each arc to consist of more than one node. The related arc-coloring extends the notion of digraph arc-coloring, which has been studied by diverse authors. Using two classical results we easily prove that the optimal coloring of a digraph, as well as the 2-coloring test for every directed hypergraph, require polynomial time. Instead, the k-colorability problem for some fixed degree d is shown to be NP-complete if k ≥ d ≥ 2 and k ≥ 3, even if the input is restricted to the so-called non-overlapping hypergraphs. We also describe a subclass of hypergraphs for which the 3-colorability test is polynomially decidable. Some results are rephrased and proved using suitable adjacency matrices, namely walls.