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Seminaire MASCOTTEEulerian and Hamiltonian Dicycles in Directed Hypergraphs
par Guillaume Ducoffe
| Date : | 20/11/12 | | Time : | 10:30 | | Location : | Galois Coriolis |
We generalize the concepts of Eulerian and Hamiltonian digraphs to directed hypergraphs. A dihypergraph H is a pair (V(H),E(H)), where V(H) is a non- empty set of elements, called vertices, and E(H) is a collection of ordered pairs of subsets of V(H), called hyperarcs. It is Eulerian (resp. Hamiltonian) if there is a dicycle containing each hyperarc (resp. each vertex) exactly once. We first present some properties of Eulerian and Hamiltonian dihypergraphs. Especially, we study when iterated line dihypergraphs are Eulerian and Hamiltonian. Finally, we study when the generalized de Bruijn dihypergraphs are Eulerian and Hamiltonian.
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