A Meyniel-Type Condition for Bipancyclicity in Balanced Bipartite Digraphs

Abstract

We prove that a strongly connected balanced bipartite digraph $D$ of order $2a$, $a\geq3$, satisfying $d(u)+d(v)\geq 3a$ for every pair of vertices $u,v$ with a common in-neighbour or a common out-neighbour, is either bipancyclic or a directed cycle of length $2a$.