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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)