Sufficient conditions for Hamiltonian cycles in bipartite digraphs

Abstract

We prove two sufficient conditions for Hamiltonian cycles in balanced bipartite digraphs. Let D be a strongly connected balanced bipartite digraph of order 2a. Then:(i) Ifa≥4andmax{d(x),d(y)}≥2a−1for every pair of vertices{x,y}with a common out-neighbour, then eitherDis Hamiltonian orDis isomorphic to a certain digraph of order eight which we specify.(ii) Ifa≥4andd(x)+d(y)≥4a−3for every pair of vertices{x,y}with a common out-neighbour, thenDis Hamiltonian.The first result improves a theorem of Wang and the second result, in particular, establishes a conjecture due to Bang-Jensen, Gutin and Li for strongly connected balanced bipartite digraphs of orders at least eight.