Hamiltonian Cycles and Hamiltonian-biconnectedness in Bipartite Digraphs

Let D denote a balanced bipartite digraph with 2n vertices and for each vertex x, d+(x) ≥ k, d−(x) ≥ k, k ≥ 1, such that the maxi-mum cardinality of a balanced independent set is 2β and n = 2β + k. We give two functions F (n, β) and G(n, β) such that if D has at least F (n, β) (resp. G(n, β)) arcs, then it is hamiltonian (resp. hamiltonian-biconnected). Key words and phrases: hamiltonian cycles, bipartite digraphs, hamiltonian-biconnectedness. Resumen Sea D un digrafo bipartito balanceado de orden 2n. Supongamos que para todo vértice x, d+(x) ≥ k, d−(x) ≥ k, k ≥ 1. Sea 2β la máxima cardinalidad de los conjuntos independientes balanceados y sea n = 2β+k. Damos dos funciones F (n, β) y G(n, β) tal que si D tiene a