On ordered directed ρ-labelings of bipartite digraphs and cyclic digraph decompositions

摘要

It is known that an ordered ρ-labeling of a bipartite graph G with n edges yields a cyclic G-decomposition of K_(2nx+1) for every positive integer x. We extend the concept of an ordered ρ-labeling to bipartite digraphs and show that an ordered directed ρ-labeling of a bipartite digraph D with n arcs yields a cyclic D- decomposition of K_(nx+1)~* for every positive integer x. We also find several classes of bipartite digraphs that admit an ordered directed ρ-labeling.