par Cowling, Peter 
Référence Discrete mathematics, 167-168, page (215-236)
Publication Publié, 1997-04
Référence Discrete mathematics, 167-168, page (215-236)
Publication Publié, 1997-04
Article révisé par les pairs
| Résumé : | Let H be a hypergraph with vertices V(H) and hyperedges E(H). The total graph of H, T(H), is the simple graph with vertex set V(H) ∪ E(H) where vertices x and y of T(H) are adjacent if and only if x is contained in, contains or is adjacent to y in H. We give a simple characterisation of those graphs which are the total graphs of some hypergraphs. We show that the total graph uniquely defines a linear hypergraph up to isomorphism and duality and present examples to show that this is not the case for general nonlinear hypergraphs. We give a polynomial time algorithm for the problem of deciding whether a given graph is the total graph of a linear hypergraph. |
