The Longest Paths and Cycles in Bipartite Oriented Graphs

Abstract:

      Let D be a bipartite oriented graph in which the indegree and outdegree of each vertex are at least k. The result given in this paper is that D contains either a cycle of length at least 4k or a path of length at least 4k 1. Jackson [1] declared that: if |V(D) |≤4k,D contains a Hamiltonian cycle. Evidently, the result Of this paper implies the result given by Jackson.