In an oriented graph G, a vertex v is said to be a "second neighbour" of a vertex u if v is not an out-neighbour of u, but is an out-neighbour of an out-neighbour of u. The second neighbourhood conjecture, due to Seymour, states that in every oriented graph there exists a vertex u that has at least as many second neighbours as out-neighbours. In this talk, we shall see some proofs for this conjecture for some special classes of oriented graphs.
