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Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 olte s gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell if it consists of two complete graphs sharing exactly one common… (More)

The eeects of the vertex push operation (when a vertex is pushed, the direction of each of its incident arcs is reversed) on the connec-tivity of tournaments are studied. It is shown that there exists an n k such that any tournament with n vertices, n n k , can be made k-strongly connected using pushes, for any k 1. These results imply, for example, that… (More)

- M Knor, L Niepel, L ˇ Soltés
- 1992

For a graph G such that L 2 (G) is not empty, we construct a supergraph H such that C(L i (H)) = L i (G) for all i, 0≤i≤2. Here L i (G) denotes the i-iterated line graph of G and C(G) denotes the subgraph of G induced by central nodes. This result is, in a sense, best possible since we provide an infinite class of graphs G such that L i (G) = C(L i (H)) for… (More)